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class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Electrons"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Electrons</span> </div> </a> <ul id="toc-Electrons-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Radiation_theory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Radiation_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Radiation theory</span> </div> </a> <ul id="toc-Radiation_theory-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Old_quantum_theory" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Old_quantum_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Old quantum theory</span> </div> </a> <button aria-controls="toc-Old_quantum_theory-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Old quantum theory subsection</span> </button> <ul id="toc-Old_quantum_theory-sublist" class="vector-toc-list"> <li id="toc-Max_Planck_introduces_quanta_to_explain_black-body_radiation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Max_Planck_introduces_quanta_to_explain_black-body_radiation"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Max Planck introduces quanta to explain black-body radiation</span> </div> </a> <ul id="toc-Max_Planck_introduces_quanta_to_explain_black-body_radiation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Albert_Einstein_applies_quanta_to_explain_the_photoelectric_effect" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Albert_Einstein_applies_quanta_to_explain_the_photoelectric_effect"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Albert Einstein applies quanta to explain the photoelectric effect</span> </div> </a> <ul id="toc-Albert_Einstein_applies_quanta_to_explain_the_photoelectric_effect-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quantization_of_matter:_the_Bohr_model_of_the_atom" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Quantization_of_matter:_the_Bohr_model_of_the_atom"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Quantization of matter: the Bohr model of the atom</span> </div> </a> <ul id="toc-Quantization_of_matter:_the_Bohr_model_of_the_atom-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Spin_quantization" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Spin_quantization"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Spin quantization</span> </div> </a> <ul id="toc-Spin_quantization-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-de_Broglie's_matter_wave_hypothesis" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#de_Broglie's_matter_wave_hypothesis"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>de Broglie's matter wave hypothesis</span> </div> </a> <ul id="toc-de_Broglie's_matter_wave_hypothesis-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Development_of_modern_quantum_mechanics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Development_of_modern_quantum_mechanics"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Development of modern quantum mechanics</span> </div> </a> <button aria-controls="toc-Development_of_modern_quantum_mechanics-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Development of modern quantum mechanics subsection</span> </button> <ul id="toc-Development_of_modern_quantum_mechanics-sublist" class="vector-toc-list"> <li id="toc-Matrix_mechanics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Matrix_mechanics"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Matrix mechanics</span> </div> </a> <ul id="toc-Matrix_mechanics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Schrödinger_and_the_wave_mechanics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Schrödinger_and_the_wave_mechanics"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Schrödinger and the wave mechanics</span> </div> </a> <ul id="toc-Schrödinger_and_the_wave_mechanics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Copenhagen_interpretation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Copenhagen_interpretation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Copenhagen interpretation</span> </div> </a> <ul id="toc-Copenhagen_interpretation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Application_to_the_hydrogen_atom" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Application_to_the_hydrogen_atom"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Application to the hydrogen atom</span> </div> </a> <ul id="toc-Application_to_the_hydrogen_atom-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dirac,_relativity,_and_development_of_the_formal_methods" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Dirac,_relativity,_and_development_of_the_formal_methods"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5</span> <span>Dirac, relativity, and development of the formal methods</span> </div> </a> <ul id="toc-Dirac,_relativity,_and_development_of_the_formal_methods-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Quantum_field_theory" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Quantum_field_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Quantum field theory</span> </div> </a> <ul id="toc-Quantum_field_theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quantum_information" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Quantum_information"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Quantum information</span> </div> </a> <ul id="toc-Quantum_information-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Founding_experiments" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Founding_experiments"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Founding experiments</span> </div> </a> <ul id="toc-Founding_experiments-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" 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Available in 23 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-23" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">23 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D8%A7%D8%B1%D9%8A%D8%AE_%D9%85%D9%8A%D9%83%D8%A7%D9%86%D9%8A%D9%83%D8%A7_%D8%A7%D9%84%D9%83%D9%85" title="تاريخ ميكانيكا الكم – Arabic" lang="ar" hreflang="ar" data-title="تاريخ ميكانيكا الكم" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%95%E0%A7%8B%E0%A6%AF%E0%A6%BC%E0%A6%BE%E0%A6%A8%E0%A7%8D%E0%A6%9F%E0%A6%BE%E0%A6%AE_%E0%A6%AC%E0%A6%B2%E0%A6%AC%E0%A6%BF%E0%A6%9C%E0%A7%8D%E0%A6%9E%E0%A6%BE%E0%A6%A8%E0%A7%87%E0%A6%B0_%E0%A6%87%E0%A6%A4%E0%A6%BF%E0%A6%B9%E0%A6%BE%E0%A6%B8" title="কোয়ান্টাম বলবিজ্ঞানের ইতিহাস – Bangla" lang="bn" hreflang="bn" data-title="কোয়ান্টাম বলবিজ্ঞানের ইতিহাস" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Hist%C3%B2ria_de_la_mec%C3%A0nica_qu%C3%A0ntica" title="Història de la mecànica quàntica – Catalan" lang="ca" hreflang="ca" data-title="Història de la mecànica quàntica" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-da badge-Q17559452 badge-recommendedarticle mw-list-item" title="recommended article"><a href="https://da.wikipedia.org/wiki/Kvantemekanikkens_historie" title="Kvantemekanikkens historie – Danish" lang="da" hreflang="da" data-title="Kvantemekanikkens historie" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Historia_de_la_mec%C3%A1nica_cu%C3%A1ntica" title="Historia de la mecánica cuántica – Spanish" lang="es" hreflang="es" data-title="Historia de la mecánica cuántica" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Historio_de_kvantuma_mekaniko" title="Historio de kvantuma mekaniko – Esperanto" lang="eo" hreflang="eo" data-title="Historio de kvantuma mekaniko" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D8%A7%D8%B1%DB%8C%D8%AE_%D9%85%DA%A9%D8%A7%D9%86%DB%8C%DA%A9_%DA%A9%D9%88%D8%A7%D9%86%D8%AA%D9%88%D9%85%DB%8C" title="تاریخ مکانیک کوانتومی – Persian" lang="fa" hreflang="fa" data-title="تاریخ مکانیک کوانتومی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Histoire_de_la_m%C3%A9canique_quantique" title="Histoire de la mécanique quantique – French" lang="fr" hreflang="fr" data-title="Histoire de la mécanique quantique" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%96%91%EC%9E%90%EC%97%AD%ED%95%99%EC%9D%98_%EC%97%AD%EC%82%AC" title="양자역학의 역사 – Korean" lang="ko" hreflang="ko" data-title="양자역학의 역사" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%94%D7%99%D7%A1%D7%98%D7%95%D7%A8%D7%99%D7%94_%D7%A9%D7%9C_%D7%9E%D7%9B%D7%A0%D7%99%D7%A7%D7%AA_%D7%94%D7%A7%D7%95%D7%95%D7%A0%D7%98%D7%99%D7%9D" title="היסטוריה של מכניקת הקוונטים – Hebrew" lang="he" hreflang="he" data-title="היסטוריה של מכניקת הקוונטים" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Kvantin%C4%97s_mechanikos_istorija" title="Kvantinės mechanikos istorija – Lithuanian" lang="lt" hreflang="lt" data-title="Kvantinės mechanikos istorija" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/A_kvantummechanika_t%C3%B6rt%C3%A9nete" title="A kvantummechanika története – Hungarian" lang="hu" hreflang="hu" data-title="A kvantummechanika története" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6%E3%81%AE%E6%AD%B4%E5%8F%B2" title="量子力学の歴史 – Japanese" lang="ja" hreflang="ja" data-title="量子力学の歴史" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%95%E0%A9%81%E0%A8%86%E0%A8%82%E0%A8%9F%E0%A8%AE_%E0%A8%AE%E0%A8%95%E0%A9%88%E0%A8%A8%E0%A8%BF%E0%A8%95%E0%A8%B8_%E0%A8%A6%E0%A8%BE_%E0%A8%87%E0%A8%A4%E0%A8%BF%E0%A8%B9%E0%A8%BE%E0%A8%B8" title="ਕੁਆਂਟਮ ਮਕੈਨਿਕਸ ਦਾ ਇਤਿਹਾਸ – Punjabi" lang="pa" hreflang="pa" data-title="ਕੁਆਂਟਮ ਮਕੈਨਿਕਸ ਦਾ ਇਤਿਹਾਸ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%AF_%DA%A9%D9%88%D8%A7%D9%86%D9%BC%D9%88%D9%85_%D9%85%DB%8C%D8%AE%D8%A7%D9%86%DB%8C%DA%A9_%D8%AA%D8%A7%D8%B1%DB%8C%D8%AE%DA%86%D9%87" title="د کوانټوم میخانیک تاریخچه – Pashto" lang="ps" hreflang="ps" data-title="د کوانټوم میخانیک تاریخچه" 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id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Timeline_of_quantum_mechanics" title="Timeline of quantum mechanics">Timeline of quantum mechanics</a>, <a href="/wiki/History_of_physics" title="History of physics">History of physics</a>, and <a href="/wiki/History_of_quantum_field_theory" title="History of quantum field theory">History of quantum field theory</a></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:10_Quantum_Mechanics_Masters.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/10_Quantum_Mechanics_Masters.jpg/200px-10_Quantum_Mechanics_Masters.jpg" decoding="async" width="200" height="692" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/7/79/10_Quantum_Mechanics_Masters.jpg 1.5x" data-file-width="275" data-file-height="951" /></a><figcaption>10 of the most influential figures in the <b>history of quantum mechanics</b>. Left to right: <a href="/wiki/Max_Planck" title="Max Planck">Max Planck</a>, <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a>, <a href="/wiki/Niels_Bohr" title="Niels Bohr">Niels Bohr</a>, <a href="/wiki/Louis_de_Broglie" title="Louis de Broglie">Louis de Broglie</a>, <a href="/wiki/Max_Born" title="Max Born">Max Born</a>, <a href="/wiki/Paul_Dirac" title="Paul Dirac">Paul Dirac</a>, <a href="/wiki/Werner_Heisenberg" title="Werner Heisenberg">Werner Heisenberg</a>, <a href="/wiki/Wolfgang_Pauli" title="Wolfgang Pauli">Wolfgang Pauli</a>, <a href="/wiki/Erwin_Schr%C3%B6dinger" title="Erwin Schrödinger">Erwin Schrödinger</a>, <a href="/wiki/Richard_Feynman" title="Richard Feynman">Richard Feynman</a>. </figcaption></figure> <p>The history of <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a> is a fundamental part of the <a href="/wiki/History_of_physics#20th_century:_birth_of_modern_physics" title="History of physics">history of modern physics</a>. The major chapters of this history begin with the emergence of quantum ideas to explain individual phenomena—blackbody radiation, the photoelectric effect, solar emission spectra—an era called the Old or Older quantum theories.<sup id="cite_ref-Whittaker_1-0" class="reference"><a href="#cite_note-Whittaker-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Building on the technology <a href="/wiki/History_of_classical_mechanics" title="History of classical mechanics">developed in classical mechanics</a>, the invention of wave mechanics by <a href="/wiki/Erwin_Schr%C3%B6dinger" title="Erwin Schrödinger">Erwin Schrödinger</a> and expansion by many others triggers the "modern" era beginning around 1925. Paul Dirac's relativistic quantum theory work lead him to explore quantum theories of radiation, culminating in <a href="/wiki/Quantum_electrodynamics" title="Quantum electrodynamics">quantum electrodynamics</a>, the first <a href="/wiki/Quantum_field_theory" title="Quantum field theory">quantum field theory</a>. The history of quantum mechanics continues in the <a href="/wiki/History_of_quantum_field_theory" title="History of quantum field theory">history of quantum field theory</a>. The history of <a href="/wiki/Quantum_chemistry" title="Quantum chemistry">quantum chemistry</a>, theoretical basis of <a href="/wiki/Chemical_structure" title="Chemical structure">chemical structure</a>, <a href="/wiki/Chemical_reaction" title="Chemical reaction">reactivity</a>, and <a href="/wiki/Chemical_bond" title="Chemical bond">bonding</a>, interlaces with the events discussed in this article. </p><p>The phrase "quantum mechanics" was coined (in German, <i>Quantenmechanik</i>) by the group of physicists including Max Born, <a href="/wiki/Werner_Heisenberg" title="Werner Heisenberg">Werner Heisenberg</a>, and <a href="/wiki/Wolfgang_Pauli" title="Wolfgang Pauli">Wolfgang Pauli</a>, at the <a href="/wiki/University_of_G%C3%B6ttingen" title="University of Göttingen">University of Göttingen</a> in the early 1920s, and was first used in Born's 1925 paper <i>"Zur Quantenmechanik"</i>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>The word <i><a href="/wiki/Quantum" title="Quantum">quantum</a></i> comes from the <a href="/wiki/Latin_language" class="mw-redirect" title="Latin language">Latin word</a> for "how much" (as does <i>quantity</i>). Something that is <i>quantized</i>, as the energy of Planck's harmonic oscillators, can only take specific values. For example, in most countries, money is effectively quantized, with the <i>quantum of money</i> being the lowest-value coin in circulation. Mechanics is the branch of science that deals with the action of forces on objects. So, quantum mechanics is the part of mechanics that deals with objects for which particular properties are quantized. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Triumph_and_trouble_at_the_end_of_the_classical_era">Triumph and trouble at the end of the classical era</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_quantum_mechanics&action=edit&section=1" title="Edit section: Triumph and trouble at the end of the classical era"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/History_of_physics#19th_century" title="History of physics">discoveries of the 19th century</a>, both the successes and failures, set the stage for the emergence of quantum mechanics. </p> <div class="mw-heading mw-heading3"><h3 id="Wave_theory_of_light">Wave theory of light</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_quantum_mechanics&action=edit&section=2" title="Edit section: Wave theory of light"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Beginning in 1670 and progressing over three decades, <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a> developed and championed his <a href="/wiki/Corpuscular_theory" class="mw-redirect" title="Corpuscular theory">corpuscular theory</a>, arguing that the perfectly straight lines of reflection demonstrated light's particle nature, as at that time no wave theory demonstrated travel in straight lines.<sup id="cite_ref-Whittaker_1-1" class="reference"><a href="#cite_note-Whittaker-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 19">: 19 </span></sup> He explained refraction by positing that particles of light accelerated laterally upon entering a denser medium. Around the same time, Newton's contemporaries <a href="/wiki/Robert_Hooke" title="Robert Hooke">Robert Hooke</a> and <a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Christiaan Huygens</a>, and later <a href="/wiki/Augustin-Jean_Fresnel" title="Augustin-Jean Fresnel">Augustin-Jean Fresnel</a>, mathematically refined the wave viewpoint, showing that if light traveled at different speeds in different media, refraction could be easily explained as the medium-dependent propagation of light waves. The resulting <a href="/wiki/Huygens%E2%80%93Fresnel_principle" title="Huygens–Fresnel principle">Huygens–Fresnel principle</a> was extremely successful at reproducing light's behaviour and was consistent with <a href="/wiki/Thomas_Young_(scientist)" title="Thomas Young (scientist)">Thomas Young</a>'s discovery of <a href="/wiki/Wave_interference" title="Wave interference">wave interference</a> of light by his <a href="/wiki/Double-slit_experiment" title="Double-slit experiment">double-slit experiment</a> in 1801.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> The wave view did not immediately displace the ray and particle view, but began to dominate scientific thinking about light in the mid 19th century, since it could explain polarization phenomena that the alternatives could not.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">James Clerk Maxwell</a> discovered that he could apply his previously discovered <a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell's equations</a>, along with a slight modification to describe self-propagating waves of oscillating electric and magnetic fields. It quickly became apparent that visible light, ultraviolet light, and infrared light were all electromagnetic waves of differing frequency.<sup id="cite_ref-Whittaker_1-2" class="reference"><a href="#cite_note-Whittaker-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 272">: 272 </span></sup> This theory became a critical ingredient in the beginning of quantum mechanics. </p> <div class="mw-heading mw-heading3"><h3 id="Emerging_atomic_theory">Emerging atomic theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_quantum_mechanics&action=edit&section=3" title="Edit section: Emerging atomic theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>During the early 19th century, <a href="/wiki/Chemistry" title="Chemistry">chemical</a> research by <a href="/wiki/John_Dalton" title="John Dalton">John Dalton</a> and <a href="/wiki/Amedeo_Avogadro" title="Amedeo Avogadro">Amedeo Avogadro</a> lent weight to the <a href="/wiki/Atomic_theory" class="mw-redirect" title="Atomic theory">atomic theory</a> of matter, an idea that <a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">James Clerk Maxwell</a>, <a href="/wiki/Ludwig_Boltzmann" title="Ludwig Boltzmann">Ludwig Boltzmann</a> and others built upon to establish the <a href="/wiki/Kinetic_theory_of_gases" title="Kinetic theory of gases">kinetic theory of gases</a>. The successes of kinetic theory gave further credence to the idea that matter is composed of atoms, yet the theory also had shortcomings that would only be resolved by the development of quantum mechanics.<sup id="cite_ref-Feynman-kinetic-theory_6-0" class="reference"><a href="#cite_note-Feynman-kinetic-theory-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> The existence of atoms was not universally accepted among physicists or chemists; <a href="/wiki/Ernst_Mach" title="Ernst Mach">Ernst Mach</a>, for example, was a staunch anti-atomist.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Boltzmanns-molecule.jpg" class="mw-file-description"><img alt="Boltzmann's iodine molecule model" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/20/Boltzmanns-molecule.jpg/220px-Boltzmanns-molecule.jpg" decoding="async" width="220" height="228" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/20/Boltzmanns-molecule.jpg/330px-Boltzmanns-molecule.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/2/20/Boltzmanns-molecule.jpg 2x" data-file-width="421" data-file-height="436" /></a><figcaption>Ludwig Boltzmann's <b>diagram of the I<sub>2</sub> molecule</b> proposed in 1898 showing the atomic "sensitive region" (α, β) of overlap.</figcaption></figure> <p>The earliest hints of problems in classical mechanics were raised in relation to the temperature dependence of the properties of gasses.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Ludwig_Boltzmann" title="Ludwig Boltzmann">Ludwig Boltzmann</a> suggested in 1877 that the energy levels of a physical system, such as a <a href="/wiki/Molecule" title="Molecule">molecule</a>, could be discrete (rather than continuous). Boltzmann's rationale for the presence of discrete energy levels in molecules such as those of iodine gas had its origins in his <a href="/wiki/Statistical_thermodynamics" class="mw-redirect" title="Statistical thermodynamics">statistical thermodynamics</a> and <a href="/wiki/Statistical_mechanics" title="Statistical mechanics">statistical mechanics</a> theories and was backed up by <a href="/wiki/Mathematical" class="mw-redirect" title="Mathematical">mathematical</a> arguments, as would also be the case twenty years later with the first <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum theory</a> put forward by Max Planck. </p> <div class="mw-heading mw-heading3"><h3 id="Electrons">Electrons</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_quantum_mechanics&action=edit&section=4" title="Edit section: Electrons"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the final days of the 1800s, <a href="/wiki/J._J._Thomson" title="J. J. Thomson">J. J. Thomson</a> established that <a href="/wiki/Electron" title="Electron">electrons</a> carry a negative charge opposite but the same size as that of a hydrogen ion while having a mass over one thousand times less. Many such electrons were known to be associated with every atom.<sup id="cite_ref-Whittaker_1-3" class="reference"><a href="#cite_note-Whittaker-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 365">: 365 </span></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Radiation_theory">Radiation theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_quantum_mechanics&action=edit&section=5" title="Edit section: Radiation theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Black_body.svg" class="mw-file-description"><img alt="Blackbody radiation curve" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/19/Black_body.svg/220px-Black_body.svg.png" decoding="async" width="220" height="176" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/19/Black_body.svg/330px-Black_body.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/19/Black_body.svg/440px-Black_body.svg.png 2x" data-file-width="600" data-file-height="480" /></a><figcaption> With decreasing temperature, the peak of the <b>blackbody radiation</b> curve shifts to longer wavelengths and also has lower intensities. The blackbody radiation curves (1862) at left are also compared with the early, classical limit model of <a href="/wiki/John_William_Strutt,_3rd_Baron_Rayleigh" title="John William Strutt, 3rd Baron Rayleigh">Rayleigh</a> and <a href="/wiki/James_Jeans" title="James Jeans">Jeans</a> (1900) shown at right. The short wavelength side of the curves was already approximated in 1896 by the <a href="/wiki/Wien_approximation" title="Wien approximation">Wien distribution law</a>.</figcaption></figure> <p>Throughout the 1800s many studies investigated details in the <a href="/wiki/Spectral_line" title="Spectral line">spectrum</a> of intensity versus frequency for light emitted by flames, by the Sun, or red-hot objects.<sup id="cite_ref-Whittaker_1-4" class="reference"><a href="#cite_note-Whittaker-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 367">: 367 </span></sup> The <a href="/wiki/Rydberg_formula" title="Rydberg formula">Rydberg formula</a> effectively summarized the dark lines seen in the spectrum, but he provided no physical model to explain them. The spectrum emitted by red-hot objects could be explained at high or low wavelengths but the two theories differed. </p> <div class="mw-heading mw-heading2"><h2 id="Old_quantum_theory">Old quantum theory</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_quantum_mechanics&action=edit&section=6" title="Edit section: Old quantum theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Quantum mechanics developed in two distinct phases. The first phase, known as the <a href="/wiki/Old_quantum_theory" title="Old quantum theory">old quantum theory</a>, began around 1900 with radically new approaches to explanations physical phenomena not understood by classical mechanics of the 1800s.<sup id="cite_ref-Whittaker_1-5" class="reference"><a href="#cite_note-Whittaker-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Max_Planck_introduces_quanta_to_explain_black-body_radiation">Max Planck introduces quanta to explain black-body radiation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_quantum_mechanics&action=edit&section=7" title="Edit section: Max Planck introduces quanta to explain black-body radiation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Ultraviolet_catastrophe" title="Ultraviolet catastrophe">Ultraviolet catastrophe</a></div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Max_Planck_1878.GIF" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/Max_Planck_1878.GIF/170px-Max_Planck_1878.GIF" decoding="async" width="170" height="226" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/Max_Planck_1878.GIF/255px-Max_Planck_1878.GIF 1.5x, //upload.wikimedia.org/wikipedia/commons/6/62/Max_Planck_1878.GIF 2x" data-file-width="332" data-file-height="441" /></a><figcaption>A side portrait of Planck as a young adult, c. 1878</figcaption></figure> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Hot_metalwork.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Hot_metalwork.jpg/330px-Hot_metalwork.jpg" decoding="async" width="330" height="240" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Hot_metalwork.jpg/495px-Hot_metalwork.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Hot_metalwork.jpg/660px-Hot_metalwork.jpg 2x" data-file-width="1600" data-file-height="1163" /></a><figcaption>Hot metalwork. The yellow-orange glow is the visible part of the thermal radiation emitted due to the high temperature. Everything else in the picture is glowing with thermal radiation as well, but less brightly and at longer wavelengths than the human eye can detect. A far-infrared camera can observe this radiation.</figcaption></figure> <p><a href="/wiki/Thermal_radiation" title="Thermal radiation">Thermal radiation</a> is electromagnetic radiation emitted from the surface of an object due to the object's internal energy. If an object is heated sufficiently, it starts to emit light at the red end of the visible <a href="/wiki/Spectrum" title="Spectrum">spectrum</a>, as it becomes <a href="https://en.wiktionary.org/wiki/en:red-hot#English" class="extiw" title="wikt:en:red-hot">red hot</a>. </p><p>Heating it further causes the color to change from red to yellow, white, and blue, as it emits light at increasingly shorter wavelengths (higher frequencies). A perfect emitter is also a perfect absorber: when it is cold, such an object looks perfectly black, because it absorbs all the light that falls on it and emits none. Consequently, an ideal thermal emitter is known as a <a href="/wiki/Black_body" title="Black body">black body</a>, and the radiation it emits is called <a href="/wiki/Black-body_radiation" title="Black-body radiation">black-body radiation</a>. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:RWP-comparison.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/RWP-comparison.svg/220px-RWP-comparison.svg.png" decoding="async" width="220" height="176" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/RWP-comparison.svg/330px-RWP-comparison.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/72/RWP-comparison.svg/440px-RWP-comparison.svg.png 2x" data-file-width="600" data-file-height="480" /></a><figcaption>Predictions of the amount of thermal radiation of different frequencies emitted by a body. Correct values predicted by Planck's law (green) contrasted against the classical values of <a href="/wiki/Rayleigh%E2%80%93Jeans_law" title="Rayleigh–Jeans law">Rayleigh-Jeans law</a> (red) and <a href="/wiki/Wien_approximation" title="Wien approximation">Wien approximation</a> (blue).</figcaption></figure> <p>By the late 19th century, thermal radiation had been fairly well characterized experimentally. Several formulas had been created that could describe some of the experimental measurements of thermal radiation: how the wavelength at which the radiation is strongest changes with temperature is given by <a href="/wiki/Wien%27s_displacement_law" title="Wien's displacement law">Wien's displacement law</a>, the overall power emitted per unit area is given by the <a href="/wiki/Stefan%E2%80%93Boltzmann_law" title="Stefan–Boltzmann law">Stefan–Boltzmann law</a>. The best theoretical explanation of the experimental results was the Rayleigh–Jeans law, which agrees with experimental results well at large wavelengths (or, equivalently, low frequencies), but strongly disagrees at short wavelengths (or high frequencies). In fact, at short wavelengths, classical physics predicted that energy will be emitted by a hot body at an infinite rate. This result, which is clearly wrong, is known as the <a href="/wiki/Ultraviolet_catastrophe" title="Ultraviolet catastrophe">ultraviolet catastrophe</a>. However, classical physics led to the <a href="/wiki/Rayleigh%E2%80%93Jeans_law" title="Rayleigh–Jeans law">Rayleigh–Jeans law</a>, which, as shown in the figure, agrees with experimental results well at low frequencies, but strongly disagrees at high frequencies. Physicists searched for a single theory that explained all the experimental results. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Black_body.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/19/Black_body.svg/310px-Black_body.svg.png" decoding="async" width="310" height="248" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/19/Black_body.svg/465px-Black_body.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/19/Black_body.svg/620px-Black_body.svg.png 2x" data-file-width="600" data-file-height="480" /></a><figcaption>Black-body radiation intensity vs color and temperature. The rainbow bar represents visible light; 5000K objects are "white hot" by mixing differing colors of visible light. To the right is the invisible infrared. Classical theory (black curve for 5000K) fails; the other curves are correct predicted by Planck's law.</figcaption></figure> <p>The first model that was able to explain the full spectrum of thermal radiation was put forward by <a href="/wiki/Max_Planck" title="Max Planck">Max Planck</a> in 1900.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> He proposed a mathematical model in which the thermal radiation was in equilibrium with a set of <a href="/wiki/Harmonic_oscillator" title="Harmonic oscillator">harmonic oscillators</a>. To reproduce the experimental results, he had to assume that each oscillator emitted an integer number of units of energy at its single characteristic frequency, rather than being able to emit any arbitrary amount of energy. In other words, the energy emitted by an oscillator was <i>quantized</i>. The quantum of energy for each oscillator, according to Planck, was proportional to the frequency of the oscillator; the constant of proportionality is now known as the <a href="/wiki/Planck_constant" title="Planck constant">Planck constant</a>. </p><p>Planck's law was the first quantum theory in physics, and Planck won the Nobel Prize in 1918 "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta".<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> At the time, however, Planck's view was that quantization was purely a <a href="/wiki/Heuristic" title="Heuristic">heuristic</a> mathematical construct, rather than (as is now believed) a fundamental change in our understanding of the world.<sup id="cite_ref-Kragh_11-0" class="reference"><a href="#cite_note-Kragh-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Albert_Einstein_applies_quanta_to_explain_the_photoelectric_effect">Albert Einstein applies quanta to explain the photoelectric effect</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_quantum_mechanics&action=edit&section=8" title="Edit section: Albert Einstein applies quanta to explain the photoelectric effect"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Photoelectric_effect" title="Photoelectric effect">Photoelectric effect</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Photoelectric_effect_in_a_solid_-_diagram.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Photoelectric_effect_in_a_solid_-_diagram.svg/220px-Photoelectric_effect_in_a_solid_-_diagram.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Photoelectric_effect_in_a_solid_-_diagram.svg/330px-Photoelectric_effect_in_a_solid_-_diagram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Photoelectric_effect_in_a_solid_-_diagram.svg/440px-Photoelectric_effect_in_a_solid_-_diagram.svg.png 2x" data-file-width="364" data-file-height="364" /></a><figcaption>Light is shone upon the surface from the left. If the light frequency is high enough, i.e. if it delivers sufficient energy, negatively charged electrons are ejected from the metal.</figcaption></figure> <p>In 1887, <a href="/wiki/Heinrich_Hertz" title="Heinrich Hertz">Heinrich Hertz</a> observed that when light with sufficient frequency hits a metallic surface, the surface emits <a href="/wiki/Cathode_rays" class="mw-redirect" title="Cathode rays">cathode rays</a>.<sup id="cite_ref-Whittaker_1-6" class="reference"><a href="#cite_note-Whittaker-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: I:362">: I:362 </span></sup> Ten years later, J. J. Thomson showed that the many reports of cathode rays were actually "corpuscles" and they quickly came to be called <a href="/wiki/Electrons" class="mw-redirect" title="Electrons">electrons</a>. In 1902, <a href="/wiki/Philipp_Lenard" title="Philipp Lenard">Philipp Lenard</a> discovered that the maximum possible energy of an ejected electron is unrelated to its <a href="/wiki/Intensity_(physics)" title="Intensity (physics)">intensity</a>.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> This observation is at odds with classical electromagnetism, which predicts that the electron's energy should be proportional to the intensity of the incident radiation.<sup id="cite_ref-Hawking_13-0" class="reference"><a href="#cite_note-Hawking-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 24">: 24 </span></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Einstein_patentoffice.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Einstein_patentoffice.jpg/170px-Einstein_patentoffice.jpg" decoding="async" width="170" height="222" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Einstein_patentoffice.jpg/255px-Einstein_patentoffice.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Einstein_patentoffice.jpg/340px-Einstein_patentoffice.jpg 2x" data-file-width="4360" data-file-height="5699" /></a><figcaption><a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> <abbr title="circa">c.</abbr> 1905</figcaption></figure> <p>In 1905, <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> suggested that even though continuous models of light worked extremely well for time-averaged optical phenomena, for instantaneous transitions the energy in light may occur a finite number of energy quanta.<sup id="cite_ref-Eistein-photoelectric_14-0" class="reference"><a href="#cite_note-Eistein-photoelectric-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> From the introduction section of his March 1905 quantum paper "On a heuristic viewpoint concerning the emission and transformation of light", Einstein states: </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>According to the assumption to be contemplated here, when a light ray is spreading from a point, the energy is not distributed continuously over ever-increasing spaces, but consists of a finite number of "energy quanta" that are localized in points in space, move without dividing, and can be absorbed or generated only as a whole.</p></blockquote> <p>This statement has been called the most revolutionary sentence written by a physicist of the twentieth century.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Photon_energy" title="Photon energy">The energy of a single quantum</a> of light of frequency <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span> is given by the frequency multiplied by the Planck constant <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b26be3e694314bc90c3215047e4a2010c6ee184a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.339ex; height:2.176ex;" alt="{\displaystyle h}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=hf}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>h</mi> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=hf}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f39fac3593bb1e2dec0282c112c4dff7a99007f6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.492ex; height:2.509ex;" alt="{\displaystyle E=hf}"></span></dd></dl> <p>Einstein assumed a light quanta transfers all of its energy to a single electron imparting at most an energy <span class="texhtml"><i>hf</i></span> to the electron. Therefore, only the light frequency determines the maximum energy that can be imparted to the electron; the intensity of the photoemission is proportional to the light beam intensity.<sup id="cite_ref-Eistein-photoelectric_14-1" class="reference"><a href="#cite_note-Eistein-photoelectric-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p>Einstein argued that it takes a certain amount of energy, called the <i><a href="/wiki/Work_function" title="Work function">work function</a></i> and denoted by <span class="texhtml">φ</span>, to remove an electron from the metal.<sup id="cite_ref-taylor_127-9_16-0" class="reference"><a href="#cite_note-taylor_127-9-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> This amount of energy is different for each metal. If the energy of the light quanta is less than the work function, then it does not carry sufficient energy to remove the electron from the metal. The threshold frequency, <span class="texhtml"><i>f</i><sub>0</sub></span>, is the frequency of a light quanta whose energy is equal to the work function: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi =hf_{0}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> <mo>=</mo> <mi>h</mi> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi =hf_{0}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c24d760b0e2b2331f681340863d6e7b74514fc81" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.798ex; height:2.676ex;" alt="{\displaystyle \varphi =hf_{0}.}"></span></dd></dl> <p>If <span class="texhtml"><i>f</i></span> is greater than <span class="texhtml"><i>f</i><sub>0</sub></span>, the energy <span class="texhtml"><i>hf</i></span> is enough to remove an electron. The ejected electron has a <a href="/wiki/Kinetic_energy" title="Kinetic energy">kinetic energy</a>, <span class="texhtml"><i>E</i><sub>k</sub></span>, which is, at most, equal to the light energy minus the energy needed to dislodge the electron from the metal: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\text{k}}=hf-\varphi =h(f-f_{0}).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>k</mtext> </mrow> </msub> <mo>=</mo> <mi>h</mi> <mi>f</mi> <mo>−</mo> <mi>φ</mi> <mo>=</mo> <mi>h</mi> <mo stretchy="false">(</mo> <mi>f</mi> <mo>−</mo> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\text{k}}=hf-\varphi =h(f-f_{0}).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c00ee4a568968d34d86f0a16cac56505712ce4fb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:26.098ex; height:2.843ex;" alt="{\displaystyle E_{\text{k}}=hf-\varphi =h(f-f_{0}).}"></span></dd></dl> <p>Einstein's description of light as being composed of energy quanta extended Planck's notion of quantized energy, which is that a single quanta of a given frequency, <span class="texhtml"><i>f</i></span>, delivers an invariant amount of energy, <span class="texhtml"><i>hf</i></span>. In nature, single quanta are rarely encountered. The Sun and emission sources available in the 19th century emit vast amount of energy every second. The <a href="/wiki/Planck_constant" title="Planck constant">Planck constant</a>, <span class="texhtml"><i>h</i></span>, is so tiny that the amount of energy in each quanta, <span class="texhtml"><i>hf</i></span> is very very small. Light we see includes many trillions of such quanta. </p> <div class="mw-heading mw-heading3"><h3 id="Quantization_of_matter:_the_Bohr_model_of_the_atom">Quantization of matter: the Bohr model of the atom</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_quantum_mechanics&action=edit&section=9" title="Edit section: Quantization of matter: the Bohr model of the atom"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Bohr_model" title="Bohr model">Bohr model</a></div> <p>By the dawn of the 20th century, the evidence required a model of the atom with a diffuse cloud of negatively charged electrons surrounding a small, dense, positively charged <a href="/wiki/Atomic_nucleus" title="Atomic nucleus">nucleus</a>. These properties suggested a model in which electrons circle the nucleus like planets orbiting a star. The classical model of the atom is called the planetary model, or sometimes the <a href="/wiki/Rutherford_model" title="Rutherford model">Rutherford model</a>—after <a href="/wiki/Ernest_Rutherford" title="Ernest Rutherford">Ernest Rutherford</a> who proposed it in 1911, based on the <a href="/wiki/Geiger%E2%80%93Marsden_experiment" class="mw-redirect" title="Geiger–Marsden experiment">Geiger–Marsden gold foil experiment</a>, which first demonstrated the existence of the nucleus. However, it was also known that the atom in this model would be unstable: according to classical theory, orbiting electrons are undergoing centripetal acceleration, and should therefore give off electromagnetic radiation, the loss of energy also causing them to spiral toward the nucleus, colliding with it in a fraction of a second. </p><p>A second, related puzzle was the <a href="/wiki/Emission_spectrum" title="Emission spectrum">emission spectrum</a> of atoms. When a gas is heated, it gives off light only at discrete frequencies. For example, the visible light given off by <a href="/wiki/Hydrogen" title="Hydrogen">hydrogen</a> consists of four different colors, as shown in the picture below. The intensity of the light at different frequencies is also different. By contrast, white light consists of a continuous emission across the whole range of visible frequencies. By the end of the nineteenth century, a simple rule known as <a href="/wiki/Balmer_series" title="Balmer series">Balmer's formula</a> showed how the frequencies of the different lines related to each other, though without explaining why this was, or making any prediction about the intensities. The formula also predicted some additional spectral lines in ultraviolet and infrared light that had not been observed at the time. These lines were later observed experimentally, raising confidence in the value of the formula. </p> <div class="thumb tnone" style="margin-left:auto;margin-right:auto;overflow:hidden;width:auto;max-width:765px"><div class="thumbinner"><div class="noresize" style="overflow:auto"><span typeof="mw:File"><a href="/wiki/File:Emission_spectrum-H.svg" class="mw-file-description" title="Emission spectrum of hydrogen. When excited, hydrogen gas gives off light in four distinct colors (spectral lines) in the visible spectrum, as well as a number of lines in the infrared and ultraviolet."><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Emission_spectrum-H.svg/757px-Emission_spectrum-H.svg.png" decoding="async" width="757" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Emission_spectrum-H.svg/1136px-Emission_spectrum-H.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/60/Emission_spectrum-H.svg/1514px-Emission_spectrum-H.svg.png 2x" data-file-width="757" data-file-height="100" /></a></span></div><div class="thumbcaption"><div class="magnify"><a href="/wiki/File:Emission_spectrum-H.svg" title="File:Emission spectrum-H.svg"> </a></div><a href="/wiki/Emission_spectrum" title="Emission spectrum">Emission spectrum</a> of <a href="/wiki/Hydrogen" title="Hydrogen">hydrogen</a>. When excited, hydrogen gas gives off light in four distinct colors (spectral lines) in the visible spectrum, as well as a number of lines in the infrared and ultraviolet.</div></div></div> <style data-mw-deduplicate="TemplateStyles:r1214851843">.mw-parser-output .hidden-begin{box-sizing:border-box;width:100%;padding:5px;border:none;font-size:95%}.mw-parser-output .hidden-title{font-weight:bold;line-height:1.6;text-align:left}.mw-parser-output .hidden-content{text-align:left}@media all and (max-width:500px){.mw-parser-output .hidden-begin{width:auto!important;clear:none!important;float:none!important}}</style><div class="hidden-begin mw-collapsible mw-collapsed" style="border:1px #aaa solid;"><div class="hidden-title skin-nightmode-reset-color" style="text-align:center">The mathematical formula describing hydrogen's emission spectrum</div><div class="hidden-content mw-collapsible-content" style=""> <p>In 1885 the Swiss mathematician <a href="/wiki/Johann_Balmer" class="mw-redirect" title="Johann Balmer">Johann Balmer</a> discovered that each wavelength <span class="texhtml"><i>λ</i></span> (lambda) in the visible spectrum of hydrogen is related to some integer <span class="texhtml"><i>n</i></span> by the equation </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda =B\left({\frac {n^{2}}{n^{2}-4}}\right)\qquad \qquad n=3,4,5,6}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mo>=</mo> <mi>B</mi> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>4</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mspace width="2em" /> <mspace width="2em" /> <mi>n</mi> <mo>=</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> <mo>,</mo> <mn>5</mn> <mo>,</mo> <mn>6</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda =B\left({\frac {n^{2}}{n^{2}-4}}\right)\qquad \qquad n=3,4,5,6}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b934f326f434bd8f3742bad1268bfd67236c753a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:39.236ex; height:6.343ex;" alt="{\displaystyle \lambda =B\left({\frac {n^{2}}{n^{2}-4}}\right)\qquad \qquad n=3,4,5,6}"></span></dd></dl> <p>where <span class="texhtml"><i>B</i></span> is a constant Balmer determined is equal to 364.56 nm. </p><p>In 1888 <a href="/wiki/Johannes_Rydberg" title="Johannes Rydberg">Johannes Rydberg</a> generalized and greatly increased the explanatory utility of Balmer's formula. He predicted that <span class="texhtml"><i>λ</i></span> is related to two integers <span class="texhtml"><i>n</i></span> and <span class="texhtml"><i>m</i></span> according to what is now known as the <a href="/wiki/Rydberg_formula" title="Rydberg formula">Rydberg formula</a>:<sup id="cite_ref-taylor_147-8_17-0" class="reference"><a href="#cite_note-taylor_147-8-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{\lambda }}=R\left({\frac {1}{m^{2}}}-{\frac {1}{n^{2}}}\right),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>λ</mi> </mfrac> </mrow> <mo>=</mo> <mi>R</mi> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{\lambda }}=R\left({\frac {1}{m^{2}}}-{\frac {1}{n^{2}}}\right),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b3f75640a81ae9d983b101e3ad86b84709ffbdbd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:21.952ex; height:6.176ex;" alt="{\displaystyle {\frac {1}{\lambda }}=R\left({\frac {1}{m^{2}}}-{\frac {1}{n^{2}}}\right),}"></span></dd></dl> <p>where <i>R</i> is the <a href="/wiki/Rydberg_constant" title="Rydberg constant">Rydberg constant</a>, equal to 0.0110 nm<sup>−1</sup>, and <i>n</i> must be greater than <i>m</i>. </p><p>The Rydberg formula accounts for the four visible wavelengths of hydrogen by setting <span class="texhtml"><i>m</i> = 2</span> and <span class="texhtml"><i>n</i> = 3, 4, 5, 6</span>. It also predicts additional wavelengths in the emission spectrum: for <span class="texhtml"><i>m</i> = 1</span> and for <span class="texhtml"><i>n</i> > 1</span>, the emission spectrum should contain certain ultraviolet wavelengths, and for <span class="texhtml"><i>m</i> = 3</span> and <span class="texhtml"><i>n</i> > 3</span>, it should also contain certain infrared wavelengths. Experimental observation of these wavelengths came two decades later: in 1908 <a href="/wiki/Louis_Paschen" class="mw-redirect" title="Louis Paschen">Louis Paschen</a> found some of the predicted infrared wavelengths, and in 1914 <a href="/wiki/Theodore_Lyman_IV" title="Theodore Lyman IV">Theodore Lyman</a> found some of the predicted ultraviolet wavelengths.<sup id="cite_ref-taylor_147-8_17-1" class="reference"><a href="#cite_note-taylor_147-8-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p><p>Both Balmer's formula and the Rydberg formula involve integers: in modern terms, they imply that some property of the atom is quantized. Understanding exactly what this property was, and why it was quantized, was a major part of the development of quantum mechanics, as shown in the rest of this article. </p> </div></div> <p>In 1905, Albert Einstein used kinetic theory to explain <a href="/wiki/Brownian_motion" title="Brownian motion">Brownian motion</a>. French physicist <a href="/wiki/Jean_Baptiste_Perrin" title="Jean Baptiste Perrin">Jean Baptiste Perrin</a> used the model in <a href="/wiki/%C3%9Cber_die_von_der_molekularkinetischen_Theorie_der_W%C3%A4rme_geforderte_Bewegung_von_in_ruhenden_Fl%C3%BCssigkeiten_suspendierten_Teilchen" title="Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen">Einstein's paper</a> to experimentally determine the mass, and the dimensions, of atoms, thereby giving direct empirical verification of the atomic theory.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (July 2023)">citation needed</span></a></i>]</sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Bohr_model_3.jpg" class="mw-file-description"><img alt="Bohr model of hydrogen atom" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Bohr_model_3.jpg/220px-Bohr_model_3.jpg" decoding="async" width="220" height="207" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Bohr_model_3.jpg/330px-Bohr_model_3.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/46/Bohr_model_3.jpg/440px-Bohr_model_3.jpg 2x" data-file-width="1943" data-file-height="1829" /></a><figcaption> <a href="/wiki/Niels_Bohr" title="Niels Bohr">Niels Bohr</a>'s 1913 quantum model of the hydrogen atom.</figcaption></figure> <p>In 1913 Niels Bohr proposed <a href="/wiki/Bohr_model" title="Bohr model">a new model of the atom</a> that included quantized electron orbits: electrons still orbit the nucleus much as planets orbit around the Sun, but they are permitted to inhabit only certain orbits, not to orbit at any arbitrary distance.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> When an atom emitted (or absorbed) energy, the electron did not move in a continuous trajectory from one orbit around the nucleus to another, as might be expected classically. Instead, the electron would jump instantaneously from one orbit to another, giving off the emitted light in the form of a photon.<sup id="cite_ref-WorldBook_19-0" class="reference"><a href="#cite_note-WorldBook-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> The possible energies of photons given off by each element were determined by the differences in energy between the orbits, and so the emission spectrum for each element would contain a number of lines.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Niels_Bohr_-_LOC_-_ggbain_-_35303.jpg" class="mw-file-description"><img alt="Head and shoulders of a young man in a suit and tie" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Niels_Bohr_-_LOC_-_ggbain_-_35303.jpg/170px-Niels_Bohr_-_LOC_-_ggbain_-_35303.jpg" decoding="async" width="170" height="235" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Niels_Bohr_-_LOC_-_ggbain_-_35303.jpg/255px-Niels_Bohr_-_LOC_-_ggbain_-_35303.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Niels_Bohr_-_LOC_-_ggbain_-_35303.jpg/340px-Niels_Bohr_-_LOC_-_ggbain_-_35303.jpg 2x" data-file-width="3415" data-file-height="4723" /></a><figcaption>Niels Bohr as a young man</figcaption></figure> <p>Starting from only one simple assumption about the rule that the orbits must obey, the Bohr model was able to relate the observed spectral lines in the emission spectrum of hydrogen to previously known constants. In Bohr's model, the electron was not allowed to emit energy continuously and crash into the nucleus: once it was in the closest permitted orbit, it was stable forever. Bohr's model did not explain why the orbits should be quantized in that way, nor was it able to make accurate predictions for atoms with more than one electron, or to explain why some spectral lines are brighter than others. </p><p>Some fundamental assumptions of the Bohr model were soon proven wrong—but the key result that the discrete lines in emission spectra are due to some property of the electrons in atoms being quantized is correct. The way that the electrons actually behave is strikingly different from Bohr's atom, and from what we see in the world of our everyday experience; this modern quantum mechanical model of the atom is discussed <a href="#Application_to_the_hydrogen_atom">below</a>. </p> <div style="clear:both;" class=""></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214851843"><div class="hidden-begin mw-collapsible mw-collapsed" style="border:1px #aaa solid;"><div class="hidden-title skin-nightmode-reset-color" style="text-align:center">A more detailed explanation of the Bohr model</div><div class="hidden-content mw-collapsible-content" style=""> <p>Bohr theorized that the <a href="/wiki/Angular_momentum" title="Angular momentum">angular momentum</a>, <span class="texhtml"><i>L</i></span>, of an electron is quantized: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L=n{\frac {h}{2\pi }}=n\hbar }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>=</mo> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>h</mi> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>n</mi> <mi class="MJX-variant">ℏ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L=n{\frac {h}{2\pi }}=n\hbar }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6d24f25ba786b920b9ff7b177ae931a5279c3ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:15.206ex; height:5.343ex;" alt="{\displaystyle L=n{\frac {h}{2\pi }}=n\hbar }"></span></dd></dl> <p>where <span class="texhtml"><i>n</i></span> is an integer and <span class="texhtml"><i>h</i></span> and <span class="texhtml"><i>ħ</i></span> are the <a href="/wiki/Planck_constant" title="Planck constant">Planck constant</a> and Planck reduced constant respectively. Starting from this assumption, <a href="/wiki/Coulomb%27s_law" title="Coulomb's law">Coulomb's law</a> and the equations of <a href="/wiki/Uniform_circular_motion" class="mw-redirect" title="Uniform circular motion">circular motion</a> show that an electron with <span class="texhtml"><i>n</i></span> units of angular momentum orbits a proton at a distance <span class="texhtml"><i>r</i></span> given by </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r={\frac {n^{2}h^{2}}{4\pi ^{2}k_{e}me^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>4</mn> <msup> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mi>m</mi> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r={\frac {n^{2}h^{2}}{4\pi ^{2}k_{e}me^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64650963e26035c03fda36b9944dcc7205dc9001" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:14.922ex; height:6.343ex;" alt="{\displaystyle r={\frac {n^{2}h^{2}}{4\pi ^{2}k_{e}me^{2}}}}"></span>,</dd></dl> <p>where <span class="texhtml"><i>k</i><sub>e</sub></span> is the <a href="/wiki/Coulomb_constant" class="mw-redirect" title="Coulomb constant">Coulomb constant</a>, <span class="texhtml"><i>m</i></span> is the mass of an electron, and <span class="texhtml"><i>e</i></span> is the <a href="/wiki/Elementary_charge" title="Elementary charge">charge on an electron</a>. For simplicity this is written as </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r=n^{2}a_{0},\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r=n^{2}a_{0},\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6457a677b7b76f2ce0fb57f83587c55d91743f56" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.229ex; width:9.369ex; height:3.009ex;" alt="{\displaystyle r=n^{2}a_{0},\!}"></span></dd></dl> <p>where <span class="texhtml"><i>a</i><sub>0</sub></span>, called the <a href="/wiki/Bohr_radius" title="Bohr radius">Bohr radius</a>, is equal to 0.0529 nm. The Bohr radius is the radius of the smallest allowed orbit. </p><p>The energy of the electron is the sum of its <a href="/wiki/Kinetic_energy" title="Kinetic energy">kinetic</a> and <a href="/wiki/Potential_energy" title="Potential energy">potential</a> energies. The electron has kinetic energy by virtue of its actual motion around the nucleus, and potential energy because of its electromagnetic interaction with the nucleus. In the Bohr model this energy can be calculated, and is given by </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=-{\frac {k_{\mathrm {e} }e^{2}}{2a_{0}}}{\frac {1}{n^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>2</mn> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=-{\frac {k_{\mathrm {e} }e^{2}}{2a_{0}}}{\frac {1}{n^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5a28a06a087400905bb25e5f034fe09731b2ea01" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:15.115ex; height:6.009ex;" alt="{\displaystyle E=-{\frac {k_{\mathrm {e} }e^{2}}{2a_{0}}}{\frac {1}{n^{2}}}}"></span>.</dd></dl> <p>Thus Bohr's assumption that angular momentum is quantized means that an electron can inhabit only certain orbits around the nucleus and that it can have only certain energies. A consequence of these constraints is that the electron does not crash into the nucleus: it cannot continuously emit energy, and it cannot come closer to the nucleus than <i>a</i><sub>0</sub> (the Bohr radius). </p><p>An electron loses energy by jumping instantaneously from its original orbit to a lower orbit; the extra energy is emitted in the form of a photon. Conversely, an electron that absorbs a photon gains energy, hence it jumps to an orbit that is farther from the nucleus. </p><p>Each photon from glowing atomic hydrogen is due to an electron moving from a higher orbit, with radius <span class="texhtml"><i>r<sub>n</sub></i></span>, to a lower orbit, <span class="texhtml"><i>r<sub>m</sub></i></span>. The energy <span class="texhtml"><i>E</i><sub>γ</sub></span> of this photon is the difference in the energies <span class="texhtml"><i>E<sub>n</sub></i></span> and <span class="texhtml"><i>E<sub>m</sub></i></span> of the electron: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\gamma }=E_{n}-E_{m}={\frac {k_{\mathrm {e} }e^{2}}{2a_{0}}}\left({\frac {1}{m^{2}}}-{\frac {1}{n^{2}}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>γ</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>2</mn> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\gamma }=E_{n}-E_{m}={\frac {k_{\mathrm {e} }e^{2}}{2a_{0}}}\left({\frac {1}{m^{2}}}-{\frac {1}{n^{2}}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70e099d78d09c64dae9cd45f407b6bdc379c1561" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:37.213ex; height:6.343ex;" alt="{\displaystyle E_{\gamma }=E_{n}-E_{m}={\frac {k_{\mathrm {e} }e^{2}}{2a_{0}}}\left({\frac {1}{m^{2}}}-{\frac {1}{n^{2}}}\right)}"></span></dd></dl> <p>Since Planck's equation shows that the photon's energy is related to its wavelength by <span class="texhtml"><i>E</i><sub>γ</sub> = <i>hc</i>/<i>λ</i></span>, the wavelengths of light that can be emitted are given by </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{\lambda }}={\frac {k_{\mathrm {e} }e^{2}}{2a_{0}hc}}\left({\frac {1}{m^{2}}}-{\frac {1}{n^{2}}}\right).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>λ</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>2</mn> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>h</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{\lambda }}={\frac {k_{\mathrm {e} }e^{2}}{2a_{0}hc}}\left({\frac {1}{m^{2}}}-{\frac {1}{n^{2}}}\right).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc1c13f451d607c70491234beaad7e23cdcafb92" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:26.817ex; height:6.343ex;" alt="{\displaystyle {\frac {1}{\lambda }}={\frac {k_{\mathrm {e} }e^{2}}{2a_{0}hc}}\left({\frac {1}{m^{2}}}-{\frac {1}{n^{2}}}\right).}"></span></dd></dl> <p>This equation has the same form as the Rydberg formula, and predicts that the constant <span class="texhtml"><i>R</i></span> should be given by </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R={\frac {k_{\mathrm {e} }e^{2}}{2a_{0}hc}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>2</mn> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>h</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R={\frac {k_{\mathrm {e} }e^{2}}{2a_{0}hc}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/766e1c7c1572d6aeac4fcb3464b07da4a47415a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:12.138ex; height:6.176ex;" alt="{\displaystyle R={\frac {k_{\mathrm {e} }e^{2}}{2a_{0}hc}}.}"></span></dd></dl> <p>Therefore, the Bohr model of the atom can predict the emission spectrum of hydrogen in terms of fundamental constants. The model can be easily modified to account for the emission spectrum of any system consisting of a nucleus and a single electron (that is, <a href="/wiki/Ion" title="Ion">ions</a> such as He<sup>+</sup> or O<sup>7+</sup>, which contain only one electron) but cannot be extended to an atom with two electrons such as neutral helium. However, it was not able to make accurate predictions for multi-electron atoms, or to explain why some spectral lines are brighter than others. </p> </div></div> <p>An important step was taken in the evolution of quantum theory at the first <a href="/wiki/Solvay_Conference" title="Solvay Conference">Solvay Congress</a> of 1911. There the top physicists of the scientific community met to discuss the problem of “Radiation and the Quanta.” By this time the Ernest Rutherford model of the atom had been published,<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> but much of the discussion involving atomic structure revolved around the quantum model of <a href="/wiki/Arthur_Haas" class="mw-redirect" title="Arthur Haas">Arthur Haas</a> in 1910. Also, at the Solvay Congress in 1911 <a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Hendrik Lorentz</a> suggested after Einstein's talk on quantum structure that the energy of a rotator be set equal to nhv.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Heilbron1969_24-0" class="reference"><a href="#cite_note-Heilbron1969-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 244">: 244 </span></sup> This was followed by other quantum models such as the <a href="/wiki/John_William_Nicholson" title="John William Nicholson">John William Nicholson</a> model of 1912 which was nuclear and discretized angular momentum.<sup id="cite_ref-Heilbron2013_25-0" class="reference"><a href="#cite_note-Heilbron2013-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-McCormmach1966_27-0" class="reference"><a href="#cite_note-McCormmach1966-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> Nicholson had introduced the spectra into his atomic model by using the oscillations of electrons in a nuclear atom perpendicular to the orbital plane thereby maintaining stability. Nicholson's atomic spectra identified many unattributed lines in solar and nebular spectra.<sup id="cite_ref-Heilbron2013_25-1" class="reference"><a href="#cite_note-Heilbron2013-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Heilbron1969_24-1" class="reference"><a href="#cite_note-Heilbron1969-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 278">: 278 </span></sup> </p><p>In 1913, Bohr explained the <a href="/wiki/Spectral_line" title="Spectral line">spectral lines</a> of the <a href="/wiki/Hydrogen_atom" title="Hydrogen atom">hydrogen atom</a>, again by using quantization, in his paper of July 1913 <i>On the Constitution of Atoms and Molecules</i> in which he discussed and cited the Nicholson model.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-McCormmach1966_27-1" class="reference"><a href="#cite_note-McCormmach1966-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> In the <a href="/wiki/Bohr_model" title="Bohr model">Bohr model</a>, the hydrogen atom is pictured as a heavy, positively charged nucleus orbited by a light, negatively charged electron. The electron can only exist in certain, discretely separated orbits, labeled by their <a href="/wiki/Angular_momentum" title="Angular momentum">angular momentum</a>, which is restricted to be an integer multiple of the <a href="/wiki/Reduced_Planck_constant" class="mw-redirect" title="Reduced Planck constant">reduced Planck constant</a>. The model's key success lay in explaining the Rydberg formula for the spectral <a href="/wiki/Hydrogen_spectral_series" title="Hydrogen spectral series">emission lines</a> of atomic hydrogen by using the transitions of electrons between orbits.<sup id="cite_ref-Heilbron1969_24-2" class="reference"><a href="#cite_note-Heilbron1969-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 276">: 276 </span></sup> While the Rydberg formula had been known experimentally, it did not gain a theoretical underpinning until the Bohr model was introduced. Not only did the Bohr model explain the reasons for the structure of the Rydberg formula, it also provided a justification for the fundamental physical constants that make up the formula's empirical results. </p><p>Moreover, the application of Planck's quantum theory to the electron allowed <a href="/wiki/%C8%98tefan_Procopiu" title="Ștefan Procopiu">Ștefan Procopiu</a> in 1911–1913, and subsequently Niels Bohr in 1913, to calculate the <a href="/wiki/Magnetic_moment" title="Magnetic moment">magnetic moment</a> of the <a href="/wiki/Electron" title="Electron">electron</a>, which was later called the "<a href="/wiki/Bohr_magneton" title="Bohr magneton">magneton</a>"; similar quantum computations, but with numerically quite different values, were subsequently made possible for both the magnetic moments of the <a href="/wiki/Proton" title="Proton">proton</a> and the <a href="/wiki/Neutron" title="Neutron">neutron</a> that are three <a href="/wiki/Order_of_magnitude" title="Order of magnitude">orders of magnitude</a> smaller than that of the electron. </p><p>These theories, though successful, were strictly <a href="/wiki/Phenomenological_model" title="Phenomenological model">phenomenological</a>: during this time, there was no rigorous justification for <a href="/wiki/Quantization_(physics)" title="Quantization (physics)">quantization</a>, aside, perhaps, from <a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Henri Poincaré</a>'s discussion of Planck's theory in his 1912 paper <span title="French-language text"><i lang="fr">Sur la théorie des quanta</i></span>.<sup id="cite_ref-McCormmach_32-0" class="reference"><a href="#cite_note-McCormmach-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Irons_33-0" class="reference"><a href="#cite_note-Irons-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> They are collectively known as the <i><a href="/wiki/Old_quantum_theory" title="Old quantum theory">old quantum theory</a></i>. </p> <div class="mw-heading mw-heading3"><h3 id="Spin_quantization">Spin quantization</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_quantum_mechanics&action=edit&section=10" title="Edit section: Spin quantization"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Spin_(physics)" title="Spin (physics)">Spin (physics)</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Stern%E2%80%93Gerlach_experiment" title="Stern–Gerlach experiment">Stern–Gerlach experiment</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><video id="mwe_player_0" poster="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Quantum_spin_and_the_Stern-Gerlach_experiment.ogv/220px--Quantum_spin_and_the_Stern-Gerlach_experiment.ogv.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" height="124" data-durationhint="91" data-mwtitle="Quantum_spin_and_the_Stern-Gerlach_experiment.ogv" data-mwprovider="wikimediacommons" resource="/wiki/File:Quantum_spin_and_the_Stern-Gerlach_experiment.ogv"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/9e/Quantum_spin_and_the_Stern-Gerlach_experiment.ogv/Quantum_spin_and_the_Stern-Gerlach_experiment.ogv.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="854" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/9e/Quantum_spin_and_the_Stern-Gerlach_experiment.ogv/Quantum_spin_and_the_Stern-Gerlach_experiment.ogv.720p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="720p.vp9.webm" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/9/9e/Quantum_spin_and_the_Stern-Gerlach_experiment.ogv" type="video/ogg; codecs="theora, vorbis"" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/9e/Quantum_spin_and_the_Stern-Gerlach_experiment.ogv/Quantum_spin_and_the_Stern-Gerlach_experiment.ogv.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="426" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/9e/Quantum_spin_and_the_Stern-Gerlach_experiment.ogv/Quantum_spin_and_the_Stern-Gerlach_experiment.ogv.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="640" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/9e/Quantum_spin_and_the_Stern-Gerlach_experiment.ogv/Quantum_spin_and_the_Stern-Gerlach_experiment.ogv.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /></video></span><figcaption>Quantum spin versus classical magnet in the <a href="/wiki/Stern%E2%80%93Gerlach_experiment" title="Stern–Gerlach experiment">Stern–Gerlach experiment</a></figcaption></figure> <p>Quantization of the orbital angular momentum of the electron combined with the magnetic moment of the electron suggested that atoms with a magnetic moment should show quantized behavior in a magnetic field. In 1922, <a href="/wiki/Otto_Stern" title="Otto Stern">Otto Stern</a> and <a href="/wiki/Walther_Gerlach" title="Walther Gerlach">Walther Gerlach</a> set out to test this theory. They heated silver in a vacuum tube equipped with a series of narrow aligned slits, creating a molecular beam of silver atoms. They shot this beam through an <a href="/wiki/Homogeneity_and_heterogeneity" title="Homogeneity and heterogeneity">inhomogeneous</a> <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic field</a>. Rather than a continuous pattern of Silver atoms, they found two bunches.<sup id="cite_ref-cigar_34-0" class="reference"><a href="#cite_note-cigar-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </p><p>Relative to its northern pole, pointing up, down, or somewhere in between, in classical mechanics, a magnet thrown through a magnetic field may be deflected a small or large distance upwards or downwards. The atoms that Stern and Gerlach shot through the magnetic field acted similarly. However, while the magnets could be deflected variable distances, the atoms would always be deflected a constant distance either up or down. This implied that the property of the atom that corresponds to the magnet's orientation must be quantized, taking one of two values (either up or down), as opposed to being chosen freely from any angle. </p><p>The choice of the orientation of the magnetic field used in the Stern–Gerlach experiment is arbitrary. In the animation shown here, the field is vertical and so the atoms are deflected either up or down. If the magnet is rotated a quarter turn, the atoms are deflected either left or right. Using a vertical field shows that the spin along the vertical axis is quantized, and using a horizontal field shows that the spin along the horizontal axis is quantized. </p><p>The results of the Stern-Gerlach experiment caused a sensation, most especially because leading scientists, including Einstein and <a href="/wiki/Paul_Ehrenfest" title="Paul Ehrenfest">Paul Ehrenfest</a> argued that the silver atoms should have random orientations in the conditions of the experiment: quantization should not have been observable.<sup id="cite_ref-cigar_34-1" class="reference"><a href="#cite_note-cigar-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> At least five years would elapse before this mystery was resolved: quantization was observed but it was not due to orbital angular momentum. </p><p>In 1925 <a href="/wiki/Ralph_Kronig" title="Ralph Kronig">Ralph Kronig</a> proposed that electrons behave as if they self-rotate, or "spin", about an axis.<sup id="cite_ref-Baggott2013_35-0" class="reference"><a href="#cite_note-Baggott2013-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 56">: 56 </span></sup> Spin would generate a tiny magnetic moment that would split the energy levels responsible for spectral lines, in agreement with existing measurements. Two electrons in the same orbital would occupy distinct <a href="/wiki/Quantum_state" title="Quantum state">quantum states</a> if they "spun" in opposite directions, thus satisfying the <a href="/wiki/Pauli_exclusion_principle" title="Pauli exclusion principle">exclusion principle</a>. Unfortunately, the theory had two significant flaws: two values computed by Kronig were off by a factor of two. Kronig's senior colleagues discouraged his work and it was never published. </p><p>Ten months later, Dutch physicists <a href="/wiki/George_Uhlenbeck" title="George Uhlenbeck">George Uhlenbeck</a> and <a href="/wiki/Samuel_Goudsmit" title="Samuel Goudsmit">Samuel Goudsmit</a> at <a href="/wiki/Leiden_University" title="Leiden University">Leiden University</a> published their theory of electron self rotation.<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> The model, like Kronig's was essentially classical but resulted in a quantum prediction. </p> <div class="mw-heading mw-heading3"><h3 id="de_Broglie's_matter_wave_hypothesis"><span id="de_Broglie.27s_matter_wave_hypothesis"></span>de Broglie's matter wave hypothesis</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_quantum_mechanics&action=edit&section=11" title="Edit section: de Broglie's matter wave hypothesis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Broglie_Big.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Broglie_Big.jpg/170px-Broglie_Big.jpg" decoding="async" width="170" height="216" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Broglie_Big.jpg/255px-Broglie_Big.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/d/d2/Broglie_Big.jpg 2x" data-file-width="300" data-file-height="381" /></a><figcaption><a href="/wiki/Louis_de_Broglie" title="Louis de Broglie">Louis de Broglie</a> in 1929. De Broglie won the <a href="/wiki/Nobel_Prize_in_Physics" title="Nobel Prize in Physics">Nobel Prize in Physics</a> for his prediction that matter acts as a wave, made in his 1924 PhD thesis.</figcaption></figure> <p>In 1924 <a href="/wiki/Louis_de_Broglie" title="Louis de Broglie">Louis de Broglie</a> published a breakthrough hypothesis: matter has wave properties. Building on Einstein's proposal that the photoelectric effect can be described using quantized energy transfers and by Einstein's separate proposal, from special relativity, that mass at rest is equivalent to energy via <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=m_{0}c^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=m_{0}c^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e379c4379411852db6472d6414fbc31a14bc46d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.03ex; height:3.009ex;" alt="{\displaystyle E=m_{0}c^{2}}"></span>, de Broglie proposed that matter in motion appears to have an associated wave with wavelength <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda =h/p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mo>=</mo> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda =h/p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53d90749442f4524695c449142b03c24d80ef986" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.125ex; height:2.843ex;" alt="{\displaystyle \lambda =h/p}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> is the matter momentum from the motion.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> Requiring his wavelength to encircle an atom, he explained quantization of Bohr's orbits.<sup id="cite_ref-Whittaker_1-7" class="reference"><a href="#cite_note-Whittaker-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 217">: 217 </span></sup> Simultaneously this showed that the wave behavior of light was essentially a quantum effect.<sup id="cite_ref-Whittaker_1-8" class="reference"><a href="#cite_note-Whittaker-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 216">: 216 </span></sup> </p><p>De Broglie expanded the <a href="/wiki/Bohr_model_of_the_atom" class="mw-redirect" title="Bohr model of the atom">Bohr model of the atom</a> by showing that an electron in orbit around a nucleus could be thought of as having wave-like properties. In particular, an electron is observed only in situations that permit a <a href="/wiki/Standing_wave" title="Standing wave">standing wave</a> around a <a href="/wiki/Atomic_nucleus" title="Atomic nucleus">nucleus</a>. An example of a standing wave is a violin string, which is fixed at both ends and can be made to vibrate. The waves created by a stringed instrument appear to oscillate in place, moving from crest to trough in an up-and-down motion. The wavelength of a standing wave is related to the length of the vibrating object and the boundary conditions. For example, because the violin string is fixed at both ends, it can carry standing waves of wavelengths <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle {\frac {2l}{n}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>l</mi> </mrow> <mi>n</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle {\frac {2l}{n}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ede0b6c5ab5793229032c6efcf0a71cc4acf1a38" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.148ex; height:3.509ex;" alt="{\textstyle {\frac {2l}{n}}}"></span>, where <i>l</i> is the length and <i>n</i> is a positive integer. De Broglie suggested that the allowed electron orbits were those for which the circumference of the orbit would be an integer number of wavelengths. The electron's wavelength, therefore, determines that only Bohr orbits of certain distances from the nucleus are possible. In turn, at any distance from the nucleus smaller than a certain value, it would be impossible to establish an orbit. The minimum possible distance from the nucleus is called the Bohr radius.<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> De Broglie's treatment of the Bohr atom was ultimately unsuccessful, but his hypothesis served as a starting point for Schrödinger's wave equation. </p><p>Matter behaving as a wave was first demonstrated experimentally for electrons: a beam of electrons can exhibit <a href="/wiki/Diffraction" title="Diffraction">diffraction</a>, just like a beam of light or a water wave. Three years after de Broglie published his hypothesis two different groups demonstrated electron diffraction. At the <a href="/wiki/University_of_Aberdeen" title="University of Aberdeen">University of Aberdeen</a>, <a href="/wiki/George_Paget_Thomson" title="George Paget Thomson">George Paget Thomson</a> and Alexander Reid passed a beam of electrons through a thin celluloid film, then later metal films, and observed the predicted interference patterns. (Alexander Reid, who was Thomson's graduate student, performed the first experiments but he died soon after in a motorcycle accident<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> and is rarely mentioned.) At <a href="/wiki/Bell_Labs" title="Bell Labs">Bell Labs</a>, <a href="/wiki/Clinton_Joseph_Davisson" class="mw-redirect" title="Clinton Joseph Davisson">Clinton Joseph Davisson</a> and <a href="/wiki/Lester_Halbert_Germer" class="mw-redirect" title="Lester Halbert Germer">Lester Halbert Germer</a> reflected an electron beam from a nickel sample in their experiment, observing well-defined beams predicted by wave models returning form the crystal.<sup id="cite_ref-Whittaker_1-9" class="reference"><a href="#cite_note-Whittaker-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: II:218">: II:218 </span></sup> De Broglie was awarded the <a href="/wiki/Nobel_Prize_in_Physics" title="Nobel Prize in Physics">Nobel Prize in Physics</a> in 1929 for his hypothesis; Thomson and Davisson shared the Nobel Prize for Physics in 1937 for their experimental work. </p><p>Building on de Broglie's approach, modern quantum mechanics was born in 1925, when the German physicists Werner Heisenberg, Max Born, and <a href="/wiki/Pascual_Jordan" title="Pascual Jordan">Pascual Jordan</a><sup id="cite_ref-Edwards79_41-0" class="reference"><a href="#cite_note-Edwards79-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Edwards81_42-0" class="reference"><a href="#cite_note-Edwards81-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> developed <a href="/wiki/Matrix_mechanics" title="Matrix mechanics">matrix mechanics</a> and the Austrian physicist Erwin Schrödinger invented <a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">wave mechanics</a> and the non-relativistic Schrödinger equation as an approximation of the generalised case of de Broglie's theory.<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> Schrödinger subsequently showed that the two approaches were equivalent. The first applications of quantum mechanics to physical systems were the algebraic determination of the hydrogen spectrum by Wolfgang Pauli<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> and the treatment of diatomic molecules by <a href="/wiki/Lucy_Mensing" title="Lucy Mensing">Lucy Mensing</a>.<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Development_of_modern_quantum_mechanics">Development of modern quantum mechanics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_quantum_mechanics&action=edit&section=12" title="Edit section: Development of modern quantum mechanics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The end of the first era of quantum mechanics was triggered by de Broglie's publication of his hypothesis of <a href="/wiki/Matter_wave" title="Matter wave">matter waves</a>,<sup id="cite_ref-Whittaker_1-10" class="reference"><a href="#cite_note-Whittaker-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 268">: 268 </span></sup> leading to Schrödinger's discovery of wave mechanics for matter. Accurate predictions of the absorption spectrum of hydrogen ensured wide acceptance of the new quantum theory.<sup id="cite_ref-Whittaker_1-11" class="reference"><a href="#cite_note-Whittaker-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 275">: 275 </span></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Matrix_mechanics">Matrix mechanics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_quantum_mechanics&action=edit&section=13" title="Edit section: Matrix mechanics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Matrix_mechanics" title="Matrix mechanics">matrix mechanics</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Umdeutung_paper" title="Umdeutung paper">Umdeutung paper</a></div> <p>In 1925, Werner Heisenberg attempted to solve one of the problems that the Bohr model left unanswered, explaining the intensities of the different lines in the hydrogen emission spectrum. Through a series of mathematical analogies, he wrote out the quantum-mechanical analog for the classical computation of intensities.<sup id="cite_ref-Heisenberg1925_46-0" class="reference"><a href="#cite_note-Heisenberg1925-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> Shortly afterward, Heisenberg's colleague Max Born realized that Heisenberg's method of calculating the probabilities for transitions between the different energy levels could best be expressed by using the mathematical concept of <a href="/wiki/Matrix_(mathematics)" title="Matrix (mathematics)">matrices</a>. </p><p>Heisenberg formulated an early version of the <a href="/wiki/Uncertainty_principle" title="Uncertainty principle">uncertainty principle</a> in 1927, analyzing a <a href="/wiki/Thought_experiment" title="Thought experiment">thought experiment</a> where one attempts to <a href="/wiki/Heisenberg%27s_microscope" title="Heisenberg's microscope">measure an electron's position and momentum simultaneously</a>. However, Heisenberg did not give precise mathematical definitions of what the "uncertainty" in these measurements meant, a step that would be taken soon after by <a href="/wiki/Earle_Hesse_Kennard" title="Earle Hesse Kennard">Earle Hesse Kennard</a>, Wolfgang Pauli, and <a href="/wiki/Hermann_Weyl" title="Hermann Weyl">Hermann Weyl</a>.<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Schrödinger_and_the_wave_mechanics"><span id="Schr.C3.B6dinger_and_the_wave_mechanics"></span>Schrödinger and the wave mechanics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_quantum_mechanics&action=edit&section=14" title="Edit section: Schrödinger and the wave mechanics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/History_of_variational_principles_in_physics" title="History of variational principles in physics">History of variational principles in physics</a></div> <p>In the first half of 1926, building on de Broglie's hypothesis, Erwin Schrödinger developed the equation that describes the behavior of a quantum-mechanical wave.<sup id="cite_ref-SchrBiog_49-0" class="reference"><a href="#cite_note-SchrBiog-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> The mathematical model, called the Schrödinger equation after its creator, is central to quantum mechanics, defines the permitted stationary states of a quantum system, and describes how the quantum state of a physical system changes in time.<sup id="cite_ref-EB-SchrEquation_50-0" class="reference"><a href="#cite_note-EB-SchrEquation-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> The wave itself is described by a mathematical function known as a "<a href="/wiki/Wave_function" title="Wave function">wave function</a>". Schrödinger said that the wave function provides the "means for predicting the probability of measurement results".<sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> </p><p>Schrödinger was able to calculate the energy levels of hydrogen by treating a hydrogen atom's electron as a classical wave, moving in a well of the electrical potential created by the proton. This calculation accurately reproduced the energy levels of the Bohr model. </p><p>In May 1926, Schrödinger proved that Heisenberg's <a href="/wiki/Matrix_mechanics" title="Matrix mechanics">matrix mechanics</a> and his own wave mechanics made the same predictions about the properties and behavior of the electron; mathematically, the two theories had an underlying common form. Yet the two men disagreed on the interpretation of their mutual theory. For instance, Heisenberg accepted the theoretical prediction of jumps of electrons between orbitals in an atom,<sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> but Schrödinger hoped that a theory based on continuous wave-like properties could avoid what he called (as paraphrased by <a href="/wiki/Wilhelm_Wien" title="Wilhelm Wien">Wilhelm Wien</a>) "this nonsense about quantum jumps".<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> In the end, Heisenberg's approach won out, and quantum jumps were confirmed.<sup id="cite_ref-nytimesQuantumJump_54-0" class="reference"><a href="#cite_note-nytimesQuantumJump-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Copenhagen_interpretation">Copenhagen interpretation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_quantum_mechanics&action=edit&section=15" title="Edit section: Copenhagen interpretation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Copenhagen_interpretation" title="Copenhagen interpretation">Copenhagen interpretation</a></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Niels_Bohr_Institute_1.jpg" class="mw-file-description"><img alt="A block-shaped beige building with a sloped, red-tiled roof" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Niels_Bohr_Institute_1.jpg/220px-Niels_Bohr_Institute_1.jpg" decoding="async" width="220" height="145" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Niels_Bohr_Institute_1.jpg/330px-Niels_Bohr_Institute_1.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/28/Niels_Bohr_Institute_1.jpg/440px-Niels_Bohr_Institute_1.jpg 2x" data-file-width="2048" data-file-height="1349" /></a><figcaption>The <a href="/wiki/Niels_Bohr_Institute" title="Niels Bohr Institute">Niels Bohr Institute</a> in Copenhagen, which was a focal point for researchers in quantum mechanics and related subjects in the 1920s and 1930s. Most of the world's best known theoretical physicists spent time there.</figcaption></figure> <p>Bohr, Heisenberg, and others tried to explain what these experimental results and mathematical models really mean. The term <i><a href="/wiki/Copenhagen_interpretation" title="Copenhagen interpretation">Copenhagen interpretation</a></i> has been applied to their views in retrospect, glossing over differences among them.<sup id="cite_ref-Faye-Stanford_55-0" class="reference"><a href="#cite_note-Faye-Stanford-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-camilleri2015_56-0" class="reference"><a href="#cite_note-camilleri2015-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-58" class="reference"><a href="#cite_note-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-59" class="reference"><a href="#cite_note-59"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Mermin_2017_60-0" class="reference"><a href="#cite_note-Mermin_2017-60"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup> While no definitive statement of "the" Copenhagen interpretation exists, the following ideas are widely seen as characteristic of it. </p> <ol><li>A system is completely described by a quantum state (Heisenberg)</li> <li>How the quantum state changes over time is given by a wave equation, the <a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger equation</a> imparting wave characteristics to light and matter.</li> <li>Atomic interactions are discontinuous (Planck referred to a "<a href="/wiki/Planck_constant" title="Planck constant">quantum of action</a>").</li> <li>The description of nature is essentially probabilistic. The probability of an event—for example, where on the screen a particle shows up in the double-slit experiment—is related to the square of the absolute value of the amplitude of its wave function. (<a href="/wiki/Born_rule" title="Born rule">Born rule</a>, due to <a href="/wiki/Max_Born" title="Max Born">Max Born</a>, which gives a physical meaning to the wave function in the Copenhagen interpretation: the <a href="/wiki/Probability_amplitude" title="Probability amplitude">probability amplitude</a>)</li> <li>The values of incompatible pairs of properties of the system cannot be known at the same time. (Heisenberg's <a href="/wiki/Uncertainty_principle" title="Uncertainty principle">uncertainty principle</a>)</li> <li>Matter, like light, exhibits a wave-particle duality. An experiment can demonstrate the particle-like properties of matter, or its wave-like properties; but not both at the same time. (<a href="/wiki/Complementarity_principle" class="mw-redirect" title="Complementarity principle">Complementarity principle</a> due to Bohr<sup id="cite_ref-Bohr1928English_61-0" class="reference"><a href="#cite_note-Bohr1928English-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup>)</li> <li>Measuring devices are essentially classical devices and measure classical properties such as position and momentum.</li> <li>The quantum mechanical description of large systems should closely approximate the classical description. (<a href="/wiki/Correspondence_principle" title="Correspondence principle">Correspondence principle</a> of Bohr and Heisenberg)</li></ol> <div class="mw-heading mw-heading3"><h3 id="Application_to_the_hydrogen_atom">Application to the hydrogen atom</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_quantum_mechanics&action=edit&section=16" title="Edit section: Application to the hydrogen atom"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Atomic_orbital_model" class="mw-redirect" title="Atomic orbital model">Atomic orbital model</a></div> <p>Bohr's model of the atom was essentially a planetary one, with the electrons orbiting around the nuclear "sun". However, the uncertainty principle states that an electron cannot simultaneously have an exact location and velocity in the way that a planet does. Instead of classical orbits, electrons are said to inhabit <i><a href="/wiki/Atomic_orbital" title="Atomic orbital">atomic orbitals</a></i>. An orbital is the "cloud" of possible locations in which an electron might be found, a distribution of probabilities rather than a precise location.<sup id="cite_ref-Pauling_62-0" class="reference"><a href="#cite_note-Pauling-62"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup> Each orbital is three dimensional, rather than the two-dimensional orbit, and is often depicted as a three-dimensional region within which there is a 95 percent probability of finding the electron.<sup id="cite_ref-EB-orbital_63-0" class="reference"><a href="#cite_note-EB-orbital-63"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup> </p><p>Schrödinger was able to calculate the energy levels of hydrogen by treating a hydrogen atom's electron as a wave, represented by the "<a href="/wiki/Wave_function" title="Wave function">wave function</a>" <span class="texhtml"><i>Ψ</i></span>, in an <a href="/wiki/Electric_potential" title="Electric potential">electric potential</a> <a href="/wiki/Potential_well" title="Potential well">well</a>, <span class="texhtml"><i>V</i></span>, created by the proton. The solutions to Schrödinger's equation <sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title=""There should be slightly more detail about exactly what the equation says. A reader should be able to roughly imagine what the evolution described by the equation looks like" (November 2019)">clarification needed</span></a></i>]</sup> are distributions of probabilities for electron positions and locations. Orbitals have a range of different shapes in three dimensions. The energies of the different orbitals can be calculated, and they accurately match the energy levels of the Bohr model. </p><p>Within Schrödinger's picture, each electron has four properties: </p> <ol><li>An "orbital" designation, indicating whether the particle-wave is one that is closer to the nucleus with less energy or one that is farther from the nucleus with more energy;</li> <li>The "shape" of the orbital, spherical or otherwise;</li> <li>The "inclination" of the orbital, determining the magnetic moment of the orbital around the <span class="texhtml"><i>z</i></span>-axis.</li> <li>The "spin" of the electron.</li></ol><p> The collective name for these properties is the <a href="/wiki/Quantum_state" title="Quantum state">quantum state</a> of the electron. The quantum state can be described by giving a number to each of these properties; these are known as the electron's <a href="/wiki/Quantum_numbers" class="mw-redirect" title="Quantum numbers">quantum numbers</a>. The quantum state of the electron is described by its wave function. The Pauli exclusion principle demands that no two electrons within an atom may have the same values of all four numbers. </p><figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Atomic_orbitals_spdf_m-eigenstates.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8f/Atomic_orbitals_spdf_m-eigenstates.png/330px-Atomic_orbitals_spdf_m-eigenstates.png" decoding="async" width="330" height="189" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8f/Atomic_orbitals_spdf_m-eigenstates.png/495px-Atomic_orbitals_spdf_m-eigenstates.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8f/Atomic_orbitals_spdf_m-eigenstates.png/660px-Atomic_orbitals_spdf_m-eigenstates.png 2x" data-file-width="2800" data-file-height="1600" /></a><figcaption>The shapes of atomic orbitals. Rows: 1<i>s</i>, 2<i>p</i>, 3<i>d</i> and 4<i>f</i>. From left to right <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m=-l,\ldots ,l}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mo>−</mo> <mi>l</mi> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>l</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m=-l,\ldots ,l}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d1eb098d37cfd28b0e2aed54e05dcae553bf023" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.512ex; height:2.509ex;" alt="{\displaystyle m=-l,\ldots ,l}"></span>. The colors show the phase of the wave function.</figcaption></figure> <p>The first property describing the orbital is the <a href="/wiki/Principal_quantum_number" title="Principal quantum number">principal quantum number</a>, <span class="texhtml"><i>n</i></span>, which is the same as in the Bohr model. <span class="texhtml"><i>n</i></span> denotes the energy level of each orbital. The possible values for <span class="texhtml"><i>n</i></span> are integers: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n=1,2,3\ldots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>…</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=1,2,3\ldots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/758aab790b00c1fc1640d549c30f04c6a7472bbc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.159ex; height:2.509ex;" alt="{\displaystyle n=1,2,3\ldots }"></span></dd></dl> <p>The next quantum number, the <a href="/wiki/Azimuthal_quantum_number" title="Azimuthal quantum number">azimuthal quantum number</a>, denoted <span class="texhtml"><i>l</i></span>, describes the shape of the orbital. The shape is a consequence of the <a href="/wiki/Angular_momentum" title="Angular momentum">angular momentum</a> of the orbital. The angular momentum represents the resistance of a spinning object to speeding up or slowing down under the influence of external force. The azimuthal quantum number represents the orbital angular momentum of an electron around its nucleus. The possible values for <span class="texhtml"><i>l</i></span> are integers from 0 to <span class="texhtml"><i>n − 1</i></span> (where <span class="texhtml"><i>n</i></span> is the principal quantum number of the electron): </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle l=0,1,\ldots ,n-1.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>n</mi> <mo>−</mo> <mn>1.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l=0,1,\ldots ,n-1.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70399991c59858af674a906796e312ef175d79ae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.373ex; height:2.509ex;" alt="{\displaystyle l=0,1,\ldots ,n-1.}"></span></dd></dl> <p>The shape of each orbital is usually referred to by a letter, rather than by its azimuthal quantum number. The first shape (<span class="texhtml"><i>l</i></span>=0) is denoted by the letter <span class="texhtml"><i>s</i></span> (a <a href="/wiki/Mnemonic" title="Mnemonic">mnemonic</a> being "<i>s</i>phere"). The next shape is denoted by the letter <span class="texhtml"><i>p</i></span> and has the form of a dumbbell. The other orbitals have more complicated shapes (see <a href="/wiki/Atomic_orbital" title="Atomic orbital">atomic orbital</a>), and are denoted by the letters <span class="texhtml"><i>d</i></span>, <span class="texhtml"><i>f</i></span>, <span class="texhtml"><i>g</i></span>, etc. </p><p>The third quantum number, the <a href="/wiki/Magnetic_quantum_number" title="Magnetic quantum number">magnetic quantum number</a>, describes the magnetic moment of the electron, and is denoted by <span class="texhtml"><i>m</i><sub><i>l</i></sub></span> (or simply <i>m</i>). The possible values for <span class="texhtml"><i>m</i><sub><i>l</i></sub></span> are integers from <span class="texhtml">−<i>l</i></span> to <span class="texhtml"><i>l</i></span> (where <span class="texhtml"><i>l</i></span> is the azimuthal quantum number of the electron): </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{l}=-l,-(l-1),\ldots ,0,\ldots ,(l-1),l.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mi>l</mi> <mo>,</mo> <mo>−</mo> <mo stretchy="false">(</mo> <mi>l</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mo stretchy="false">(</mo> <mi>l</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>,</mo> <mi>l</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{l}=-l,-(l-1),\ldots ,0,\ldots ,(l-1),l.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e1ccf8064a6a41409697fd695ca710a048a659a6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:38.109ex; height:2.843ex;" alt="{\displaystyle m_{l}=-l,-(l-1),\ldots ,0,\ldots ,(l-1),l.}"></span></dd></dl> <p>The magnetic quantum number measures the component of the angular momentum in a particular direction. The choice of direction is arbitrary; conventionally the z-direction is chosen. </p><p>The fourth quantum number, the <a href="/wiki/Spin_quantum_number" title="Spin quantum number">spin quantum number</a> (pertaining to the "orientation" of the electron's spin) is denoted <span class="texhtml"><i>m<sub>s</sub></i></span>, with values +<style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="frac"><span class="num">1</span>⁄<span class="den">2</span></span> or −<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">2</span></span>. </p><p>The chemist <a href="/wiki/Linus_Pauling" title="Linus Pauling">Linus Pauling</a> wrote, by way of example: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>In the case of a <a href="/wiki/Helium" title="Helium">helium</a> atom with two electrons in the 1<i>s</i> orbital, the Pauli Exclusion Principle requires that the two electrons differ in the value of one quantum number. Their values of <span class="texhtml"><i>n</i></span>, <span class="texhtml"><i>l</i></span>, and <span class="texhtml"><i>m<sub>l</sub></i></span> are the same. Accordingly they must differ in the value of <span class="texhtml"><i>m<sub>s</sub></i></span>, which can have the value of +<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">2</span></span> for one electron and −<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">2</span></span> for the other."<sup id="cite_ref-Pauling_62-1" class="reference"><a href="#cite_note-Pauling-62"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup></p></blockquote> <p>It is the underlying structure and symmetry of atomic orbitals, and the way that electrons fill them, that leads to the organization of the <a href="/wiki/Periodic_table" title="Periodic table">periodic table</a>. The way the atomic orbitals on different atoms combine to form <a href="/wiki/Molecular_orbital" title="Molecular orbital">molecular orbitals</a> determines the structure and strength of chemical bonds between atoms. </p><p>The field of <a href="/wiki/Quantum_chemistry" title="Quantum chemistry">quantum chemistry</a> was pioneered by physicists <a href="/wiki/Walter_Heitler" title="Walter Heitler">Walter Heitler</a> and <a href="/wiki/Fritz_London" title="Fritz London">Fritz London</a>, who published a study of the <a href="/wiki/Covalent_bond" title="Covalent bond">covalent bond</a> of the <a href="/wiki/Hydrogen_molecule" class="mw-redirect" title="Hydrogen molecule">hydrogen molecule</a> in 1927. Quantum chemistry was subsequently developed by a large number of workers, including the American theoretical chemist <a href="/wiki/Linus_Pauling" title="Linus Pauling">Linus Pauling</a> at <a href="/wiki/Caltech" class="mw-redirect" title="Caltech">Caltech</a>, and <a href="/wiki/John_C._Slater" title="John C. Slater">John C. Slater</a> into various theories such as Molecular Orbital Theory or Valence Theory. </p> <div class="mw-heading mw-heading3"><h3 id="Dirac,_relativity,_and_development_of_the_formal_methods"><span id="Dirac.2C_relativity.2C_and_development_of_the_formal_methods"></span>Dirac, relativity, and development of the formal methods</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_quantum_mechanics&action=edit&section=17" title="Edit section: Dirac, relativity, and development of the formal methods"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Starting around 1927, Paul Dirac began the process of unifying quantum mechanics with <a href="/wiki/Special_relativity" title="Special relativity">special relativity</a> by proposing the <a href="/wiki/Dirac_equation" title="Dirac equation">Dirac equation</a> for the electron. The Dirac equation achieves the relativistic description of the wavefunction of an electron that Schrödinger failed to obtain. It predicts electron spin and led Dirac to predict the existence of the <a href="/wiki/Positron" title="Positron">positron</a>. He also pioneered the use of operator theory, including the influential <a href="/wiki/Bra%E2%80%93ket_notation" title="Bra–ket notation">bra–ket notation</a>, as described in his famous 1930 textbook. During the same period, Hungarian polymath <a href="/wiki/John_von_Neumann" title="John von Neumann">John von Neumann</a> formulated the rigorous mathematical basis for quantum mechanics as the theory of linear operators on Hilbert spaces, as described in his <a href="/wiki/Mathematical_Foundations_of_Quantum_Mechanics" title="Mathematical Foundations of Quantum Mechanics">likewise famous 1932 textbook</a>. These, like many other works from the founding period, still stand, and remain widely used. </p> <div class="mw-heading mw-heading2"><h2 id="Quantum_field_theory">Quantum field theory</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_quantum_mechanics&action=edit&section=18" title="Edit section: Quantum field theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Beginning in 1927, researchers attempted to apply quantum mechanics to fields instead of single particles, resulting in quantum field theories. Early workers in this area include <a href="/wiki/Paul_Dirac" title="Paul Dirac">P.A.M. Dirac</a>, W. Pauli, <a href="/wiki/Victor_Weisskopf" title="Victor Weisskopf">V. Weisskopf</a>, and <a href="/wiki/Pascual_Jordan" title="Pascual Jordan">P. Jordan</a>. This area of research culminated in the formulation of <a href="/wiki/Quantum_electrodynamics" title="Quantum electrodynamics">quantum electrodynamics</a> by <a href="/wiki/Richard_Feynman" title="Richard Feynman">R.P. Feynman</a>, <a href="/wiki/Freeman_Dyson" title="Freeman Dyson">F. Dyson</a>, <a href="/wiki/Julian_Schwinger" title="Julian Schwinger">J. Schwinger</a>, and <a href="/wiki/Shin%27ichir%C5%8D_Tomonaga" title="Shin'ichirō Tomonaga">S. Tomonaga</a> during the 1940s. Quantum electrodynamics describes a quantum theory of electrons, <a href="/wiki/Positron" title="Positron">positrons</a>, and the <a href="/wiki/Electromagnetic_field" title="Electromagnetic field">electromagnetic field</a>, and served as a model for subsequent <a href="/wiki/Quantum_field_theory" title="Quantum field theory">quantum field theories</a>.<sup id="cite_ref-Edwards79_41-1" class="reference"><a href="#cite_note-Edwards79-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Edwards81_42-1" class="reference"><a href="#cite_note-Edwards81-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-64" class="reference"><a href="#cite_note-64"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Feynmann_Diagram_Gluon_Radiation.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Feynmann_Diagram_Gluon_Radiation.svg/264px-Feynmann_Diagram_Gluon_Radiation.svg.png" decoding="async" width="264" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Feynmann_Diagram_Gluon_Radiation.svg/396px-Feynmann_Diagram_Gluon_Radiation.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Feynmann_Diagram_Gluon_Radiation.svg/528px-Feynmann_Diagram_Gluon_Radiation.svg.png 2x" data-file-width="400" data-file-height="250" /></a><figcaption>Feynman diagram of <b><a href="/wiki/Gluon" title="Gluon">gluon</a> <a href="/wiki/Radiation" title="Radiation">radiation</a></b> in <a href="/wiki/Quantum_chromodynamics" title="Quantum chromodynamics">quantum chromodynamics</a></figcaption></figure> <p>The theory of <a href="/wiki/Quantum_chromodynamics" title="Quantum chromodynamics">quantum chromodynamics</a> was formulated beginning in the early 1960s. The theory as we know it today was formulated by <a href="/wiki/H._David_Politzer" class="mw-redirect" title="H. David Politzer">Politzer</a>, <a href="/wiki/David_J._Gross" class="mw-redirect" title="David J. Gross">Gross</a> and <a href="/wiki/Frank_Wilczek" title="Frank Wilczek">Wilczek</a> in 1975. </p><p>Building on pioneering work by <a href="/wiki/Julian_Schwinger" title="Julian Schwinger">Schwinger</a>, <a href="/wiki/Peter_Higgs" title="Peter Higgs">Higgs</a> and <a href="/wiki/Jeffrey_Goldstone" title="Jeffrey Goldstone">Goldstone</a>, the physicists <a href="/wiki/Sheldon_Glashow" title="Sheldon Glashow">Glashow</a>, <a href="/wiki/Steven_Weinberg" title="Steven Weinberg">Weinberg</a> and <a href="/wiki/Abdus_Salam" title="Abdus Salam">Salam</a> independently showed how the weak nuclear force and quantum electrodynamics could be merged into a single <a href="/wiki/Electroweak_force" class="mw-redirect" title="Electroweak force">electroweak force</a>, for which they received the 1979 Nobel Prize in Physics. </p> <div class="mw-heading mw-heading2"><h2 id="Quantum_information">Quantum information</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_quantum_mechanics&action=edit&section=19" title="Edit section: Quantum information"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Timeline_of_quantum_computing_and_communication" title="Timeline of quantum computing and communication">Timeline of quantum computing and communication</a></div> <p><a href="/wiki/Quantum_information_science" title="Quantum information science">Quantum information science</a> developed in the latter decades of the 20th century, beginning with theoretical results like <a href="/wiki/Holevo%27s_theorem" title="Holevo's theorem">Holevo's theorem</a>, the concept of generalized measurements or <a href="/wiki/POVM" title="POVM">POVMs</a>, the proposal of <a href="/wiki/Quantum_key_distribution" title="Quantum key distribution">quantum key distribution</a> by <a href="/wiki/BB84" title="BB84">Bennett and Brassard</a>, and <a href="/wiki/Shor%27s_algorithm" title="Shor's algorithm">Shor's algorithm</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Founding_experiments">Founding experiments</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_quantum_mechanics&action=edit&section=20" title="Edit section: Founding experiments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Thomas_Young_(scientist)" title="Thomas Young (scientist)">Thomas Young</a>'s <a href="/wiki/Double-slit_experiment" title="Double-slit experiment">double-slit experiment</a> demonstrating the wave nature of light. (c. 1801)</li> <li><a href="/wiki/Henri_Becquerel" title="Henri Becquerel">Henri Becquerel</a> discovers <a href="/wiki/Radioactivity" class="mw-redirect" title="Radioactivity">radioactivity</a>. (1896)</li> <li><a href="/wiki/J._J._Thomson" title="J. J. Thomson">J. J. Thomson</a>'s cathode ray tube experiments (discovers the electron and its negative charge). (1897)</li> <li>The study of <a href="/wiki/Black-body_radiation" title="Black-body radiation">black-body radiation</a> between 1850 and 1900, which could not be explained without quantum concepts.</li> <li>The <a href="/wiki/Photoelectric_effect" title="Photoelectric effect">photoelectric effect</a>: Einstein explained this in 1905 (and later received a Nobel prize for it) using the concept of photons, particles of light with quantized energy.</li> <li><a href="/wiki/Robert_Millikan" class="mw-redirect" title="Robert Millikan">Robert Millikan</a>'s <a href="/wiki/Oil-drop_experiment" class="mw-redirect" title="Oil-drop experiment">oil-drop experiment</a>, which showed that <a href="/wiki/Electric_charge" title="Electric charge">electric charge</a> occurs as <i><a href="/wiki/Quantum" title="Quantum">quanta</a></i> (whole units). (1909)</li> <li><a href="/wiki/Ernest_Rutherford" title="Ernest Rutherford">Ernest Rutherford</a>'s <a href="/wiki/Geiger%E2%80%93Marsden_experiment" class="mw-redirect" title="Geiger–Marsden experiment">gold foil experiment</a> disproved the plum pudding model of the <a href="/wiki/Atom" title="Atom">atom</a> which suggested that the mass and positive charge of the atom are almost uniformly distributed. This led to the planetary model of the atom (1911).</li> <li><a href="/wiki/James_Franck" title="James Franck">James Franck</a> and <a href="/wiki/Gustav_Ludwig_Hertz" title="Gustav Ludwig Hertz">Gustav Hertz's</a> <a href="/wiki/Franck%E2%80%93Hertz_experiment" title="Franck–Hertz experiment">electron collision experiment</a> shows that energy absorption by mercury atoms is quantized. (1914)</li> <li><a href="/wiki/Otto_Stern" title="Otto Stern">Otto Stern</a> and <a href="/wiki/Walther_Gerlach" title="Walther Gerlach">Walther Gerlach</a> conduct the <a href="/wiki/Stern%E2%80%93Gerlach_experiment" title="Stern–Gerlach experiment">Stern–Gerlach experiment</a>, which demonstrates the quantized nature of particle <a href="/wiki/Spin_(physics)" title="Spin (physics)">spin</a>. (1920)</li> <li><a href="/wiki/Arthur_Compton" title="Arthur Compton">Arthur Compton</a> with <a href="/wiki/Compton_scattering" title="Compton scattering">Compton scattering</a> experiment (1923)</li> <li><a href="/wiki/Clinton_Davisson" title="Clinton Davisson">Clinton Davisson</a> and <a href="/wiki/Lester_Germer" title="Lester Germer">Lester Germer</a> demonstrate the wave nature of the electron<sup id="cite_ref-65" class="reference"><a href="#cite_note-65"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup> in the <a href="/wiki/Electron_diffraction" title="Electron diffraction">electron diffraction</a> experiment. (1927)</li> <li><a href="/wiki/Carl_David_Anderson" title="Carl David Anderson">Carl David Anderson</a> with the discovery positron (1932), validated Paul Dirac's theoretical prediction of this particle (1928)</li> <li><a href="/wiki/Willis_Lamb" title="Willis Lamb">Lamb</a>–<a href="/wiki/Robert_Retherford" title="Robert Retherford">Retherford</a> experiment discovered <a href="/wiki/Lamb_shift" title="Lamb shift">Lamb shift</a> (1947), which led to the development of quantum electrodynamics.</li> <li><a href="/wiki/Clyde_L._Cowan" class="mw-redirect" title="Clyde L. Cowan">Clyde L. Cowan</a> and <a href="/wiki/Frederick_Reines" title="Frederick Reines">Frederick Reines</a> confirm the existence of the <a href="/wiki/Neutrino" title="Neutrino">neutrino</a> in the <a href="/wiki/Neutrino_experiment" class="mw-redirect" title="Neutrino experiment">neutrino experiment</a>. (1955)</li> <li><a href="/wiki/Claus_J%C3%B6nsson" title="Claus Jönsson">Claus Jönsson</a>'s double-slit experiment with electrons. (1961)</li> <li>The <a href="/wiki/Quantum_Hall_effect" title="Quantum Hall effect">quantum Hall effect</a>, discovered in 1980 by <a href="/wiki/Klaus_von_Klitzing" title="Klaus von Klitzing">Klaus von Klitzing</a>. The quantized version of the <a href="/wiki/Hall_effect" title="Hall effect">Hall effect</a> has allowed for the definition of a new practical standard for <a href="/wiki/Electrical_resistance" class="mw-redirect" title="Electrical resistance">electrical resistance</a> and for an extremely precise independent determination of the <a href="/wiki/Fine-structure_constant" title="Fine-structure constant">fine-structure constant</a>.</li> <li>The <a href="/wiki/Bell_test_experiments" class="mw-redirect" title="Bell test experiments">experimental verification</a> of <a href="/wiki/Quantum_entanglement" title="Quantum entanglement">quantum entanglement</a> by <a href="/wiki/John_Clauser" title="John Clauser">John Clauser</a> and <a href="/wiki/Stuart_Freedman" title="Stuart Freedman">Stuart Freedman</a>. (1972)</li> <li>The <a href="/wiki/Mach%E2%80%93Zehnder_interferometer" title="Mach–Zehnder interferometer">Mach–Zehnder interferometer</a> experiment conducted by <a href="/wiki/Paul_Kwiat" title="Paul Kwiat">Paul Kwiat</a>, Harold Wienfurter, Thomas Herzog, <a href="/wiki/Anton_Zeilinger" title="Anton Zeilinger">Anton Zeilinger</a>, and Mark Kasevich, providing <a href="/wiki/Elitzur%E2%80%93Vaidman_bomb-testing_problem" class="mw-redirect" title="Elitzur–Vaidman bomb-testing problem">experimental verification of the Elitzur–Vaidman bomb tester</a>, proving <a href="/wiki/Interaction-free_measurement" title="Interaction-free measurement">interaction-free measurement</a> is possible. (1994)</li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_quantum_mechanics&action=edit&section=21" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239009302">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 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molecular theory">History of molecular theory</a></li> <li><a href="/wiki/History_of_thermodynamics" title="History of thermodynamics">History of thermodynamics</a></li> <li><a href="/wiki/Timeline_of_atomic_and_subatomic_physics" title="Timeline of atomic and subatomic physics">Timeline of atomic and subatomic physics</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_quantum_mechanics&action=edit&section=22" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-Whittaker-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-Whittaker_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Whittaker_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Whittaker_1-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Whittaker_1-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-Whittaker_1-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-Whittaker_1-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-Whittaker_1-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-Whittaker_1-7"><sup><i><b>h</b></i></sup></a> <a href="#cite_ref-Whittaker_1-8"><sup><i><b>i</b></i></sup></a> <a href="#cite_ref-Whittaker_1-9"><sup><i><b>j</b></i></sup></a> <a href="#cite_ref-Whittaker_1-10"><sup><i><b>k</b></i></sup></a> <a href="#cite_ref-Whittaker_1-11"><sup><i><b>l</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFWhittaker1989" class="citation book cs1">Whittaker, Edmund T. (1989). <i>A history of the theories of aether & electricity. 2: The modern theories, 1900 - 1926</i> (Repr ed.). New York: Dover Publ. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-26126-3" title="Special:BookSources/978-0-486-26126-3"><bdi>978-0-486-26126-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+history+of+the+theories+of+aether+%26+electricity.+2%3A+The+modern+theories%2C+1900+-+1926&rft.place=New+York&rft.edition=Repr&rft.pub=Dover+Publ&rft.date=1989&rft.isbn=978-0-486-26126-3&rft.aulast=Whittaker&rft.aufirst=Edmund+T.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">Max Born, <i>My Life: Recollections of a Nobel Laureate</i>, Taylor & Francis, London, 1978. ("We became more and more convinced that a radical change of the foundations of physics was necessary, i.e., a new kind of mechanics for which we used the term quantum mechanics. This word appears for the first time in physical literature in a paper of mine...")</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFedakPrentis2009" class="citation journal cs1">Fedak, William A.; Prentis, Jeffrey J. (2009-02-01). <a rel="nofollow" class="external text" href="https://people.isy.liu.se/icg/jalar/kurser/QF/references/onBornJordan1925.pdf">"The 1925 Born and Jordan paper "On quantum mechanics"<span class="cs1-kern-right"></span>"</a> <span class="cs1-format">(PDF)</span>. <i>American Journal of Physics</i>. <b>77</b> (2): 128–139. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2009AmJPh..77..128F">2009AmJPh..77..128F</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.3009634">10.1119/1.3009634</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0002-9505">0002-9505</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=The+1925+Born+and+Jordan+paper+%22On+quantum+mechanics%22&rft.volume=77&rft.issue=2&rft.pages=128-139&rft.date=2009-02-01&rft.issn=0002-9505&rft_id=info%3Adoi%2F10.1119%2F1.3009634&rft_id=info%3Abibcode%2F2009AmJPh..77..128F&rft.aulast=Fedak&rft.aufirst=William+A.&rft.au=Prentis%2C+Jeffrey+J.&rft_id=https%3A%2F%2Fpeople.isy.liu.se%2Ficg%2Fjalar%2Fkurser%2FQF%2Freferences%2FonBornJordan1925.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFYoung1804" class="citation journal cs1">Young, Thomas (1804). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=7AZGAAAAMAAJ&pg=PA1">"Bakerian Lecture: Experiments and calculations relative to physical optics"</a>. <i>Philosophical Transactions of the Royal Society</i>. <b>94</b>: 1–16. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1804RSPT...94....1Y">1804RSPT...94....1Y</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frstl.1804.0001">10.1098/rstl.1804.0001</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:110408369">110408369</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Transactions+of+the+Royal+Society&rft.atitle=Bakerian+Lecture%3A+Experiments+and+calculations+relative+to+physical+optics&rft.volume=94&rft.pages=1-16&rft.date=1804&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A110408369%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1098%2Frstl.1804.0001&rft_id=info%3Abibcode%2F1804RSPT...94....1Y&rft.aulast=Young&rft.aufirst=Thomas&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D7AZGAAAAMAAJ%26pg%3DPA1&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBuchwald1989" class="citation book cs1">Buchwald, Jed (1989). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/riseofwavetheory0000buch"><i>The Rise of the Wave Theory of Light: Optical Theory and Experiment in the Early Nineteenth Century</i></a></span>. Chicago: University of Chicago Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-226-07886-1" title="Special:BookSources/978-0-226-07886-1"><bdi>978-0-226-07886-1</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/18069573">18069573</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Rise+of+the+Wave+Theory+of+Light%3A+Optical+Theory+and+Experiment+in+the+Early+Nineteenth+Century&rft.place=Chicago&rft.pub=University+of+Chicago+Press&rft.date=1989&rft_id=info%3Aoclcnum%2F18069573&rft.isbn=978-0-226-07886-1&rft.aulast=Buchwald&rft.aufirst=Jed&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Friseofwavetheory0000buch&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-Feynman-kinetic-theory-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-Feynman-kinetic-theory_6-0">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFeynmanLeightonSands1964" class="citation book cs1">Feynman, Richard; Leighton, Robert; Sands, Matthew (1964). <a rel="nofollow" class="external text" href="https://feynmanlectures.caltech.edu/I_40.html"><i>The Feynman Lectures on Physics</i></a>. Vol. 1. California Institute of Technology. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0201500646" title="Special:BookSources/978-0201500646"><bdi>978-0201500646</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">30 September</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Feynman+Lectures+on+Physics&rft.pub=California+Institute+of+Technology&rft.date=1964&rft.isbn=978-0201500646&rft.aulast=Feynman&rft.aufirst=Richard&rft.au=Leighton%2C+Robert&rft.au=Sands%2C+Matthew&rft_id=https%3A%2F%2Ffeynmanlectures.caltech.edu%2FI_40.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPojman2020" class="citation cs2">Pojman, Paul (2020), <a rel="nofollow" class="external text" href="https://plato.stanford.edu/archives/win2020/entries/ernst-mach/">"Ernst Mach"</a>, in Zalta, Edward N. (ed.), <i><a href="/wiki/The_Stanford_Encyclopedia_of_Philosophy" class="mw-redirect" title="The Stanford Encyclopedia of Philosophy">The Stanford Encyclopedia of Philosophy</a></i> (Winter 2020 ed.), Metaphysics Research Lab, Stanford University<span class="reference-accessdate">, retrieved <span class="nowrap">2021-09-30</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Ernst+Mach&rft.btitle=The+Stanford+Encyclopedia+of+Philosophy&rft.edition=Winter+2020&rft.pub=Metaphysics+Research+Lab%2C+Stanford+University&rft.date=2020&rft.aulast=Pojman&rft.aufirst=Paul&rft_id=https%3A%2F%2Fplato.stanford.edu%2Farchives%2Fwin2020%2Fentries%2Fernst-mach%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.feynmanlectures.caltech.edu/I_40.html">"The Feynman Lectures on Physics Vol. I Ch. 40: The Principles of Statistical Mechanics"</a>. <i>www.feynmanlectures.caltech.edu</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2024-03-10</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.feynmanlectures.caltech.edu&rft.atitle=The+Feynman+Lectures+on+Physics+Vol.+I+Ch.+40%3A+The+Principles+of+Statistical+Mechanics&rft_id=https%3A%2F%2Fwww.feynmanlectures.caltech.edu%2FI_40.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">This result was published (in German) as <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPlanck1901" class="citation journal cs1"><a href="/wiki/Max_Planck" title="Max Planck">Planck, Max</a> (1901). <a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.19013090310">"Ueber das Gesetz der Energieverteilung im Normalspectrum"</a>. <i><a href="/wiki/Annalen_der_Physik" title="Annalen der Physik">Ann. Phys.</a></i> <b>309</b> (3): 553–63. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1901AnP...309..553P">1901AnP...309..553P</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.19013090310">10.1002/andp.19013090310</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Ann.+Phys.&rft.atitle=Ueber+das+Gesetz+der+Energieverteilung+im+Normalspectrum&rft.volume=309&rft.issue=3&rft.pages=553-63&rft.date=1901&rft_id=info%3Adoi%2F10.1002%2Fandp.19013090310&rft_id=info%3Abibcode%2F1901AnP...309..553P&rft.aulast=Planck&rft.aufirst=Max&rft_id=https%3A%2F%2Fdoi.org%2F10.1002%252Fandp.19013090310&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span>. English translation: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20080418002757/http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Planck-1901/Planck-1901.html">"On the Law of Distribution of Energy in the Normal Spectrum"</a>. Archived from <a rel="nofollow" class="external text" href="http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Planck-1901/Planck-1901.html">the original</a> on 18 April 2008.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=On+the+Law+of+Distribution+of+Energy+in+the+Normal+Spectrum&rft_id=http%3A%2F%2Fdbhs.wvusd.k12.ca.us%2Fwebdocs%2FChem-History%2FPlanck-1901%2FPlanck-1901.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://nobelprize.org/nobel_prizes/physics/laureates/1918/">"The Nobel Prize in Physics 1918"</a>. <a href="/wiki/Nobel_Foundation" title="Nobel Foundation">Nobel Foundation</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2009-08-01</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Nobel+Prize+in+Physics+1918&rft.pub=Nobel+Foundation&rft_id=http%3A%2F%2Fnobelprize.org%2Fnobel_prizes%2Fphysics%2Flaureates%2F1918%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-Kragh-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-Kragh_11-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKragh2000" class="citation web cs1">Kragh, Helge (1 December 2000). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120401221617/http://physicsworld.com/cws/article/print/373">"Max Planck: the reluctant revolutionary"</a>. PhysicsWorld.com. Archived from <a rel="nofollow" class="external text" href="http://physicsworld.com/cws/article/print/373">the original</a> on 1 April 2012<span class="reference-accessdate">. Retrieved <span class="nowrap">7 December</span> 2009</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Max+Planck%3A+the+reluctant+revolutionary&rft.pub=PhysicsWorld.com&rft.date=2000-12-01&rft.aulast=Kragh&rft.aufirst=Helge&rft_id=http%3A%2F%2Fphysicsworld.com%2Fcws%2Farticle%2Fprint%2F373&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWheaton1978" class="citation journal cs1">Wheaton, Bruce R. (1978). "Philipp Lenard and the Photoelectric Effect, 1889-1911". <i>Historical Studies in the Physical Sciences</i>. <b>9</b>: 299–322. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F27757381">10.2307/27757381</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/27757381">27757381</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Historical+Studies+in+the+Physical+Sciences&rft.atitle=Philipp+Lenard+and+the+Photoelectric+Effect%2C+1889-1911&rft.volume=9&rft.pages=299-322&rft.date=1978&rft_id=info%3Adoi%2F10.2307%2F27757381&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F27757381%23id-name%3DJSTOR&rft.aulast=Wheaton&rft.aufirst=Bruce+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-Hawking-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hawking_13-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHawking2001" class="citation book cs1"><a href="/wiki/Stephen_Hawking" title="Stephen Hawking">Hawking, Stephen</a> (November 6, 2001) [November 5, 2001]. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200921192954/https://fb2bookfree.com/science/831-the-universe-in-a-nutshell.html"><i>The Universe in a Nutshell</i></a>. Vol. 55. Impey, C.D. Bantam Spectra (published April 2002). p. 80~. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.1480788">10.1063/1.1480788</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0553802023" title="Special:BookSources/978-0553802023"><bdi>978-0553802023</bdi></a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:120382028">120382028</a>. Archived from <a rel="nofollow" class="external text" href="https://fb2bookfree.com/science/831-the-universe-in-a-nutshell.html">the original</a> on September 21, 2020<span class="reference-accessdate">. Retrieved <span class="nowrap">December 14,</span> 2020</span> – via Random House Audiobooks.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Universe+in+a+Nutshell&rft.pages=80~&rft.pub=Bantam+Spectra&rft.date=2001-11-06&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A120382028%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1063%2F1.1480788&rft.isbn=978-0553802023&rft.aulast=Hawking&rft.aufirst=Stephen&rft_id=https%3A%2F%2Ffb2bookfree.com%2Fscience%2F831-the-universe-in-a-nutshell.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: </span><span class="cs1-visible-error citation-comment"><code class="cs1-code">|journal=</code> ignored (<a href="/wiki/Help:CS1_errors#periodical_ignored" title="Help:CS1 errors">help</a>)</span> <a rel="nofollow" class="external text" href="https://archive.org/details/StephenHawkingTheUniverseInANutshellBookFi">Alt URL</a></span> </li> <li id="cite_note-Eistein-photoelectric-14"><span class="mw-cite-backlink">^ <a href="#cite_ref-Eistein-photoelectric_14-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Eistein-photoelectric_14-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEinstein1905" class="citation journal cs1"><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein, Albert</a> (1905). <a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.19053220607">"Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt"</a>. <i>Annalen der Physik</i>. <b>17</b> (6): 132–48. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1905AnP...322..132E">1905AnP...322..132E</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.19053220607">10.1002/andp.19053220607</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annalen+der+Physik&rft.atitle=%C3%9Cber+einen+die+Erzeugung+und+Verwandlung+des+Lichtes+betreffenden+heuristischen+Gesichtspunkt&rft.volume=17&rft.issue=6&rft.pages=132-48&rft.date=1905&rft_id=info%3Adoi%2F10.1002%2Fandp.19053220607&rft_id=info%3Abibcode%2F1905AnP...322..132E&rft.aulast=Einstein&rft.aufirst=Albert&rft_id=https%3A%2F%2Fdoi.org%2F10.1002%252Fandp.19053220607&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span>, translated into English as <a rel="nofollow" class="external text" href="http://lorentz.phl.jhu.edu/AnnusMirabilis/AeReserveArticles/eins_lq.pdf">On a Heuristic Viewpoint Concerning the Production and Transformation of Light</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090611234106/http://lorentz.phl.jhu.edu/AnnusMirabilis/AeReserveArticles/eins_lq.pdf">Archived</a> 11 June 2009 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. The term "photon" was introduced in 1926.</span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFolsing1997" class="citation cs2">Folsing, Albrecht (1997), <i>Albert Einstein: A Biography</i>, trans. <a href="/wiki/Ewald_Osers" title="Ewald Osers">Ewald Osers</a>, Viking</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Albert+Einstein%3A+A+Biography&rft.pub=trans.+Ewald+Osers%2C+Viking&rft.date=1997&rft.aulast=Folsing&rft.aufirst=Albrecht&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-taylor_127-9-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-taylor_127-9_16-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTaylorZafiratosDubson2004" class="citation book cs1">Taylor, J. R.; Zafiratos, C. D.; Dubson, M. A. (2004). <i>Modern Physics for Scientists and Engineers</i>. Prentice Hall. pp. 127–29. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0135897890" title="Special:BookSources/0135897890"><bdi>0135897890</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Modern+Physics+for+Scientists+and+Engineers&rft.pages=127-29&rft.pub=Prentice+Hall&rft.date=2004&rft.isbn=0135897890&rft.aulast=Taylor&rft.aufirst=J.+R.&rft.au=Zafiratos%2C+C.+D.&rft.au=Dubson%2C+M.+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-taylor_147-8-17"><span class="mw-cite-backlink">^ <a href="#cite_ref-taylor_147-8_17-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-taylor_147-8_17-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTaylorZafiratosDubson2004" class="citation book cs1">Taylor, J. R.; Zafiratos, C. D.; Dubson, M. A. (2004). <i>Modern Physics for Scientists and Engineers</i>. Prentice Hall. pp. 147–48. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0135897890" title="Special:BookSources/0135897890"><bdi>0135897890</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Modern+Physics+for+Scientists+and+Engineers&rft.pages=147-48&rft.pub=Prentice+Hall&rft.date=2004&rft.isbn=0135897890&rft.aulast=Taylor&rft.aufirst=J.+R.&rft.au=Zafiratos%2C+C.+D.&rft.au=Dubson%2C+M.+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcEvoyZarate2004" class="citation book cs1">McEvoy, J. P.; Zarate, O. (2004). <i>Introducing Quantum Theory</i>. Totem Books. pp. 70–89, [89]. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1840465778" title="Special:BookSources/1840465778"><bdi>1840465778</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introducing+Quantum+Theory&rft.pages=70-89%2C+89&rft.pub=Totem+Books&rft.date=2004&rft.isbn=1840465778&rft.aulast=McEvoy&rft.aufirst=J.+P.&rft.au=Zarate%2C+O.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-WorldBook-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-WorldBook_19-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWorld_Book.Inc2007" class="citation book cs1">World Book.Inc (2007). "22". <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170130100748/http://www.worldcat.org/title/world-book-encyclopedia/oclc/894799866"><i>World Book Encyclopedia</i></a> (Electronic reproduction). The World Book encyclopedia. Vol. 22 (3 ed.). Chicago, Illinois: World Book. p. 6. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0716601074" title="Special:BookSources/978-0716601074"><bdi>978-0716601074</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/894799866">894799866</a>. Archived from <a rel="nofollow" class="external text" href="https://www.worldcat.org/oclc/894799866">the original</a> on 30 January 2017<span class="reference-accessdate">. Retrieved <span class="nowrap">December 14,</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=22&rft.btitle=World+Book+Encyclopedia&rft.place=Chicago%2C+Illinois&rft.series=The+World+Book+encyclopedia&rft.pages=6&rft.edition=3&rft.pub=World+Book&rft.date=2007&rft_id=info%3Aoclcnum%2F894799866&rft.isbn=978-0716601074&rft.au=World+Book.Inc&rft_id=https%3A%2F%2Fwww.worldcat.org%2Foclc%2F894799866&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span> <a rel="nofollow" class="external text" href="https://archive.org/details/worldbookencycl703worl">Alt URL</a></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWittkeDicke1961" class="citation book cs1">Wittke, J.P; Dicke, R.H (June 1, 1961) [1960]. "11". In Holladay, W.G. (ed.). <a rel="nofollow" class="external text" href="https://www.scribd.com/doc/124926316/Dicke-Wittke-Introduction-to-Quantum-Mechanics"><i>Introduction to Quantum Mechanics</i></a> (eBook). Vol. 16. Nashville, Tennessee: ADDISON WESLEY LONGMAN INC (published January 1, 1978). p. 10. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.3057610">10.1063/1.3057610</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0201015102" title="Special:BookSources/978-0201015102"><bdi>978-0201015102</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/53473">53473</a><span class="reference-accessdate">. Retrieved <span class="nowrap">December 14,</span> 2020</span> – via Vanderbilt University.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=11&rft.btitle=Introduction+to+Quantum+Mechanics&rft.place=Nashville%2C+Tennessee&rft.pages=10&rft.pub=ADDISON+WESLEY+LONGMAN+INC&rft.date=1961-06-01&rft_id=info%3Aoclcnum%2F53473&rft_id=info%3Adoi%2F10.1063%2F1.3057610&rft.isbn=978-0201015102&rft.aulast=Wittke&rft.aufirst=J.P&rft.au=Dicke%2C+R.H&rft_id=https%3A%2F%2Fwww.scribd.com%2Fdoc%2F124926316%2FDicke-Wittke-Introduction-to-Quantum-Mechanics&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLakhtakia1996" class="citation book cs1">Lakhtakia, A (1996). <i>Models and modelers of hydrogen : Thales, Thomson, Rutherford, Bohr, Sommerfeld, Goudsmit, Heisenberg, Schrödinger, Dirac, Sallhofer</i>. Singapore River Edge, NJ: World Scientific. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/981-02-2302-1" title="Special:BookSources/981-02-2302-1"><bdi>981-02-2302-1</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/35643527">35643527</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Models+and+modelers+of+hydrogen+%3A+Thales%2C+Thomson%2C+Rutherford%2C+Bohr%2C+Sommerfeld%2C+Goudsmit%2C+Heisenberg%2C+Schr%C3%B6dinger%2C+Dirac%2C+Sallhofer&rft.place=Singapore+River+Edge%2C+NJ&rft.pub=World+Scientific&rft.date=1996&rft_id=info%3Aoclcnum%2F35643527&rft.isbn=981-02-2302-1&rft.aulast=Lakhtakia&rft.aufirst=A&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRutherford1911" class="citation journal cs1"><a href="/wiki/Ernest_Rutherford" title="Ernest Rutherford">Rutherford, E.</a> (1911). "LXXIX. The scattering of α and β particles by matter and the structure of the atom". <i>The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science</i>. <b>21</b> (125). 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Physics Today 42.12 (1989): 34-40.</span> </li> <li id="cite_note-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-37">^</a></b></span> <span class="reference-text">Aczel, Amir D., <i>Entanglement</i>, pp. 51ff. (Penguin, 2003) <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1551926476" title="Special:BookSources/978-1551926476">978-1551926476</a></span> </li> <li id="cite_note-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-38">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcEvoyZarate2004" class="citation book cs1">McEvoy, J. P.; Zarate, O. (2004). <i>Introducing Quantum Theory</i>. 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Totem Books. p. 87. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1840465778" title="Special:BookSources/1840465778"><bdi>1840465778</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introducing+Quantum+Theory&rft.pages=87&rft.pub=Totem+Books&rft.date=2004&rft.isbn=1840465778&rft.aulast=McEvoy&rft.aufirst=J.+P.&rft.au=Zarate%2C+O.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-40"><span class="mw-cite-backlink"><b><a href="#cite_ref-40">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNavarro2010" class="citation journal cs1">Navarro, Jaume (2010). <a rel="nofollow" class="external text" href="https://www.cambridge.org/core/product/identifier/S0007087410000026/type/journal_article">"Electron diffraction chez Thomson: early responses to quantum physics in Britain"</a>. <i>The British Journal for the History of Science</i>. <b>43</b> (2): 245–275. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FS0007087410000026">10.1017/S0007087410000026</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0007-0874">0007-0874</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+British+Journal+for+the+History+of+Science&rft.atitle=Electron+diffraction+chez+Thomson%3A+early+responses+to+quantum+physics+in+Britain&rft.volume=43&rft.issue=2&rft.pages=245-275&rft.date=2010&rft_id=info%3Adoi%2F10.1017%2FS0007087410000026&rft.issn=0007-0874&rft.aulast=Navarro&rft.aufirst=Jaume&rft_id=https%3A%2F%2Fwww.cambridge.org%2Fcore%2Fproduct%2Fidentifier%2FS0007087410000026%2Ftype%2Fjournal_article&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-Edwards79-41"><span class="mw-cite-backlink">^ <a href="#cite_ref-Edwards79_41-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Edwards79_41-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEdwards1979" class="citation journal cs1">Edwards, David A. (1979). "The mathematical foundations of quantum mechanics". <i>Synthese</i>. <b>42</b> (1). Springer Science and Business Media LLC: 1–70. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fbf00413704">10.1007/bf00413704</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0039-7857">0039-7857</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:46969028">46969028</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Synthese&rft.atitle=The+mathematical+foundations+of+quantum+mechanics&rft.volume=42&rft.issue=1&rft.pages=1-70&rft.date=1979&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A46969028%23id-name%3DS2CID&rft.issn=0039-7857&rft_id=info%3Adoi%2F10.1007%2Fbf00413704&rft.aulast=Edwards&rft.aufirst=David+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-Edwards81-42"><span class="mw-cite-backlink">^ <a href="#cite_ref-Edwards81_42-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Edwards81_42-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEdwards1981" class="citation journal cs1">Edwards, David A. (1981). "Mathematical foundations of quantum field theory: Fermions, gauge fields, and supersymmetry part I: Lattice field theories". <i>International Journal of Theoretical Physics</i>. <b>20</b> (7). Springer Science and Business Media LLC: 503–517. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1981IJTP...20..503E">1981IJTP...20..503E</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fbf00669437">10.1007/bf00669437</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0020-7748">0020-7748</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:120108219">120108219</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Journal+of+Theoretical+Physics&rft.atitle=Mathematical+foundations+of+quantum+field+theory%3A+Fermions%2C+gauge+fields%2C+and+supersymmetry+part+I%3A+Lattice+field+theories&rft.volume=20&rft.issue=7&rft.pages=503-517&rft.date=1981&rft_id=info%3Adoi%2F10.1007%2Fbf00669437&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A120108219%23id-name%3DS2CID&rft.issn=0020-7748&rft_id=info%3Abibcode%2F1981IJTP...20..503E&rft.aulast=Edwards&rft.aufirst=David+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-43">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHanle1977" class="citation cs2">Hanle, P. A. (December 1977), "Erwin Schrodinger's Reaction to Louis de Broglie's Thesis on the Quantum Theory.", <i>Isis</i>, <b>68</b> (4): 606–609, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F351880">10.1086/351880</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:121913205">121913205</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Isis&rft.atitle=Erwin+Schrodinger%27s+Reaction+to+Louis+de+Broglie%27s+Thesis+on+the+Quantum+Theory.&rft.volume=68&rft.issue=4&rft.pages=606-609&rft.date=1977-12&rft_id=info%3Adoi%2F10.1086%2F351880&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A121913205%23id-name%3DS2CID&rft.aulast=Hanle&rft.aufirst=P.+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-44"><span class="mw-cite-backlink"><b><a href="#cite_ref-44">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPauli1926" class="citation journal cs1 cs1-prop-foreign-lang-source">Pauli, Wolfgang (1926-05-01). "Über das Wasserstoffspektrum vom Standpunkt der neuen Quantenmechanik". <i>Zeitschrift für Physik</i> (in German). <b>36</b> (5): 336–363. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1926ZPhy...36..336P">1926ZPhy...36..336P</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01450175">10.1007/BF01450175</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0044-3328">0044-3328</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:128132824">128132824</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Zeitschrift+f%C3%BCr+Physik&rft.atitle=%C3%9Cber+das+Wasserstoffspektrum+vom+Standpunkt+der+neuen+Quantenmechanik&rft.volume=36&rft.issue=5&rft.pages=336-363&rft.date=1926-05-01&rft_id=info%3Adoi%2F10.1007%2FBF01450175&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A128132824%23id-name%3DS2CID&rft.issn=0044-3328&rft_id=info%3Abibcode%2F1926ZPhy...36..336P&rft.aulast=Pauli&rft.aufirst=Wolfgang&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-45"><span class="mw-cite-backlink"><b><a href="#cite_ref-45">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMensing1926" class="citation journal cs1 cs1-prop-foreign-lang-source">Mensing, Lucy (1926-11-01). "Die Rotations-Schwingungsbanden nach der Quantenmechanik". <i>Zeitschrift für Physik</i> (in German). <b>36</b> (11): 814–823. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1926ZPhy...36..814M">1926ZPhy...36..814M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01400216">10.1007/BF01400216</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0044-3328">0044-3328</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:123240532">123240532</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Zeitschrift+f%C3%BCr+Physik&rft.atitle=Die+Rotations-Schwingungsbanden+nach+der+Quantenmechanik&rft.volume=36&rft.issue=11&rft.pages=814-823&rft.date=1926-11-01&rft_id=info%3Adoi%2F10.1007%2FBF01400216&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A123240532%23id-name%3DS2CID&rft.issn=0044-3328&rft_id=info%3Abibcode%2F1926ZPhy...36..814M&rft.aulast=Mensing&rft.aufirst=Lucy&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-Heisenberg1925-46"><span class="mw-cite-backlink"><b><a href="#cite_ref-Heisenberg1925_46-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVan_der_Waerden1967" class="citation book cs1">Van der Waerden, B. L. (1967). <i>Sources of Quantum Mechanics</i>. Mineola, NY: Dover Publications. pp. 261–76. <q>Received 29 July 1925</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Sources+of+Quantum+Mechanics&rft.place=Mineola%2C+NY&rft.pages=261-76&rft.pub=Dover+Publications&rft.date=1967&rft.aulast=Van+der+Waerden&rft.aufirst=B.+L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span> See Werner Heisenberg's paper, "Quantum-Theoretical Re-interpretation of Kinematic and Mechanical Relations" pp. 261–76</span> </li> <li id="cite_note-47"><span class="mw-cite-backlink"><b><a href="#cite_ref-47">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBuschLahtiWerner2013" class="citation journal cs1"><a href="/wiki/Paul_Busch_(physicist)" title="Paul Busch (physicist)">Busch, Paul</a>; Lahti, Pekka; Werner, Reinhard F. (17 October 2013). "Proof of Heisenberg's Error-Disturbance Relation". <i>Physical Review Letters</i>. <b>111</b> (16): 160405. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1306.1565">1306.1565</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2013PhRvL.111p0405B">2013PhRvL.111p0405B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.111.160405">10.1103/PhysRevLett.111.160405</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0031-9007">0031-9007</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/24182239">24182239</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:24507489">24507489</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Proof+of+Heisenberg%27s+Error-Disturbance+Relation&rft.volume=111&rft.issue=16&rft.pages=160405&rft.date=2013-10-17&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A24507489%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2013PhRvL.111p0405B&rft_id=info%3Aarxiv%2F1306.1565&rft.issn=0031-9007&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.111.160405&rft_id=info%3Apmid%2F24182239&rft.aulast=Busch&rft.aufirst=Paul&rft.au=Lahti%2C+Pekka&rft.au=Werner%2C+Reinhard+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-48"><span class="mw-cite-backlink"><b><a href="#cite_ref-48">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAppleby2016" class="citation journal cs1">Appleby, David Marcus (6 May 2016). <a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Fe18050174">"Quantum Errors and Disturbances: Response to Busch, Lahti and Werner"</a>. <i>Entropy</i>. <b>18</b> (5): 174. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1602.09002">1602.09002</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2016Entrp..18..174A">2016Entrp..18..174A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Fe18050174">10.3390/e18050174</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Entropy&rft.atitle=Quantum+Errors+and+Disturbances%3A+Response+to+Busch%2C+Lahti+and+Werner&rft.volume=18&rft.issue=5&rft.pages=174&rft.date=2016-05-06&rft_id=info%3Aarxiv%2F1602.09002&rft_id=info%3Adoi%2F10.3390%2Fe18050174&rft_id=info%3Abibcode%2F2016Entrp..18..174A&rft.aulast=Appleby&rft.aufirst=David+Marcus&rft_id=https%3A%2F%2Fdoi.org%2F10.3390%252Fe18050174&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-SchrBiog-49"><span class="mw-cite-backlink"><b><a href="#cite_ref-SchrBiog_49-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNobel_Prize_Organization" class="citation web cs1">Nobel Prize Organization. <a rel="nofollow" class="external text" href="https://www.nobelprize.org/nobel_prizes/physics/laureates/1933/schrodinger-bio.html">"Erwin Schrödinger – Biographical"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">28 March</span> 2014</span>. <q>His great discovery, Schrödinger's wave equation, was made at the end of this epoch-during the first half of 1926.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Erwin+Schr%C3%B6dinger+%E2%80%93+Biographical&rft.au=Nobel+Prize+Organization&rft_id=https%3A%2F%2Fwww.nobelprize.org%2Fnobel_prizes%2Fphysics%2Flaureates%2F1933%2Fschrodinger-bio.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-EB-SchrEquation-50"><span class="mw-cite-backlink"><b><a href="#cite_ref-EB-SchrEquation_50-0">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.britannica.com/EBchecked/topic/528298/Schrodinger-equation">"Schrodinger Equation (Physics)", <i>Encyclopædia Britannica </i></a></span> </li> <li id="cite_note-51"><span class="mw-cite-backlink"><b><a href="#cite_ref-51">^</a></b></span> <span class="reference-text">Erwin Schrödinger, "The Present Situation in Quantum Mechanics", p. 9. "This translation was originally published in Proceedings of the American Philosophical Society, 124, 323–38, and then appeared as Section I.11 of Part I of Quantum Theory and Measurement (J. A. Wheeler and W. H. Zurek, eds., Princeton University Press, NJ 1983). This paper can be downloaded here: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFErwin_Schrödinger" class="citation web cs1">Erwin Schrödinger. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20101113223658/http://www.tu-harburg.de/rzt/rzt/it/QM/cat.html">"A Translation of Schrödinger's "Cat Paradox Paper"<span class="cs1-kern-right"></span>"</a>. Translated by John D. Trimmer. Archived from <a rel="nofollow" class="external text" href="http://www.tu-harburg.de/rzt/rzt/it/QM/cat.html">the original</a> on 2010-11-13.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=A+Translation+of+Schr%C3%B6dinger%27s+%22Cat+Paradox+Paper%22&rft.au=Erwin+Schr%C3%B6dinger&rft_id=http%3A%2F%2Fwww.tu-harburg.de%2Frzt%2Frzt%2Fit%2FQM%2Fcat.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-52"><span class="mw-cite-backlink"><b><a href="#cite_ref-52">^</a></b></span> <span class="reference-text">Heisenberg, W. (1955). The development of the interpretation of the quantum theory, pp. 12–29 in <i>Niels Bohr and the Development of Physics: Essays dedicated to Niels Bohr on the occasion of his seventieth birthday</i>, edited by <a href="/wiki/Wolfgang_Pauli" title="Wolfgang Pauli">Pauli, W.</a> with the assistance of <a href="/wiki/L%C3%A9on_Rosenfeld" title="Léon Rosenfeld">Rosenfeld, L.</a> and <a href="/wiki/Victor_Weisskopf" title="Victor Weisskopf">Weisskopf, V.</a>, Pergamon, London, p. 13: "the single quantum jump ... is "factual" in nature".</span> </li> <li id="cite_note-53"><span class="mw-cite-backlink"><b><a href="#cite_ref-53">^</a></b></span> <span class="reference-text">W. Moore, <i>Schrödinger: Life and Thought</i>, Cambridge University Press (1989), p. 222. See p. 227 for Schrödinger's own words.</span> </li> <li id="cite_note-nytimesQuantumJump-54"><span class="mw-cite-backlink"><b><a href="#cite_ref-nytimesQuantumJump_54-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGleick1986" class="citation news cs1">Gleick, James (21 October 1986). <a rel="nofollow" class="external text" href="https://www.nytimes.com/1986/10/21/science/physicists-finally-get-to-see-quantum-jump-with-own-eyes.html">"Physicists finally get to see quantum jump with own eyes"</a>. <i>The New York Times</i><span class="reference-accessdate">. Retrieved <span class="nowrap">30 November</span> 2019</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+New+York+Times&rft.atitle=Physicists+finally+get+to+see+quantum+jump+with+own+eyes&rft.date=1986-10-21&rft.aulast=Gleick&rft.aufirst=James&rft_id=https%3A%2F%2Fwww.nytimes.com%2F1986%2F10%2F21%2Fscience%2Fphysicists-finally-get-to-see-quantum-jump-with-own-eyes.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-Faye-Stanford-55"><span class="mw-cite-backlink"><b><a href="#cite_ref-Faye-Stanford_55-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFaye2019" class="citation book cs1"><a href="/wiki/Jan_Faye" title="Jan Faye">Faye, Jan</a> (2019). <a rel="nofollow" class="external text" href="https://plato.stanford.edu/entries/qm-copenhagen/">"Copenhagen Interpretation of Quantum Mechanics"</a>. In Zalta, Edward N. (ed.). <i><a href="/wiki/Stanford_Encyclopedia_of_Philosophy" title="Stanford Encyclopedia of Philosophy">Stanford Encyclopedia of Philosophy</a></i>. Metaphysics Research Lab, Stanford University.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Copenhagen+Interpretation+of+Quantum+Mechanics&rft.btitle=Stanford+Encyclopedia+of+Philosophy&rft.pub=Metaphysics+Research+Lab%2C+Stanford+University&rft.date=2019&rft.aulast=Faye&rft.aufirst=Jan&rft_id=https%3A%2F%2Fplato.stanford.edu%2Fentries%2Fqm-copenhagen%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-camilleri2015-56"><span class="mw-cite-backlink"><b><a href="#cite_ref-camilleri2015_56-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCamilleriSchlosshauer2015" class="citation journal cs1">Camilleri, K.; Schlosshauer, M. (2015). "Niels Bohr as Philosopher of Experiment: Does Decoherence Theory Challenge Bohr's Doctrine of Classical Concepts?". <i>Studies in History and Philosophy of Modern Physics</i>. <b>49</b>: 73–83. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1502.06547">1502.06547</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2015SHPMP..49...73C">2015SHPMP..49...73C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.shpsb.2015.01.005">10.1016/j.shpsb.2015.01.005</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:27697360">27697360</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Studies+in+History+and+Philosophy+of+Modern+Physics&rft.atitle=Niels+Bohr+as+Philosopher+of+Experiment%3A+Does+Decoherence+Theory+Challenge+Bohr%27s+Doctrine+of+Classical+Concepts%3F&rft.volume=49&rft.pages=73-83&rft.date=2015&rft_id=info%3Aarxiv%2F1502.06547&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A27697360%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1016%2Fj.shpsb.2015.01.005&rft_id=info%3Abibcode%2F2015SHPMP..49...73C&rft.aulast=Camilleri&rft.aufirst=K.&rft.au=Schlosshauer%2C+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-57"><span class="mw-cite-backlink"><b><a href="#cite_ref-57">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOmnès1999" class="citation book cs1"><a href="/wiki/Roland_Omn%C3%A8s" title="Roland Omnès">Omnès, Roland</a> (1999). "The Copenhagen Interpretation". <i>Understanding Quantum Mechanics</i>. Princeton University Press. pp. 41–54. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2Fj.ctv173f2pm.9">10.2307/j.ctv173f2pm.9</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:203390914">203390914</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+Copenhagen+Interpretation&rft.btitle=Understanding+Quantum+Mechanics&rft.pages=41-54&rft.pub=Princeton+University+Press&rft.date=1999&rft_id=info%3Adoi%2F10.2307%2Fj.ctv173f2pm.9&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A203390914%23id-name%3DS2CID&rft.aulast=Omn%C3%A8s&rft.aufirst=Roland&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-58"><span class="mw-cite-backlink"><b><a href="#cite_ref-58">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFScheibe1973" class="citation book cs1"><a href="/wiki/Erhard_Scheibe" title="Erhard Scheibe">Scheibe, Erhard</a> (1973). <i>The Logical Analysis of Quantum Mechanics</i>. Pergamon Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780080171586" title="Special:BookSources/9780080171586"><bdi>9780080171586</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/799397091">799397091</a>. <q>[T]here is no point in looking for <i>the</i> Copenhagen interpretation as a unified and consistent logical structure. Terms such as "Copenhagen interpretation" or "Copenhagen school" are based on the history of the development of quantum mechanics; they form a simplified and often convenient way of referring to the ideas of a number of physicists who played an important role in the establishment of quantum mechanics, and who were collaborators of Bohr's at his Institute or took part in the discussions during the crucial years. On closer inspection, one sees quite easily that these ideas are divergent in detail and that in particular the views of Bohr, the spiritual leader of the school, form a separate entity which can now be understood only by a thorough study of as many as possible of the relevant publications by Bohr himself.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Logical+Analysis+of+Quantum+Mechanics&rft.pub=Pergamon+Press&rft.date=1973&rft_id=info%3Aoclcnum%2F799397091&rft.isbn=9780080171586&rft.aulast=Scheibe&rft.aufirst=Erhard&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-59"><span class="mw-cite-backlink"><b><a href="#cite_ref-59">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPeres2002" class="citation journal cs1"><a href="/wiki/Asher_Peres" title="Asher Peres">Peres, Asher</a> (2002). "Popper's experiment and the Copenhagen interpretation". <i><a href="/wiki/Studies_in_History_and_Philosophy_of_Modern_Physics" class="mw-redirect" title="Studies in History and Philosophy of Modern Physics">Studies in History and Philosophy of Modern Physics</a></i>. <b>33</b>: 23. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/quant-ph/9910078">quant-ph/9910078</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1999quant.ph.10078P">1999quant.ph.10078P</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS1355-2198%2801%2900034-X">10.1016/S1355-2198(01)00034-X</a>. <q>There seem to be at least as many different Copenhagen interpretations as people who use that term; probably there are more.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Studies+in+History+and+Philosophy+of+Modern+Physics&rft.atitle=Popper%27s+experiment+and+the+Copenhagen+interpretation&rft.volume=33&rft.pages=23&rft.date=2002&rft_id=info%3Aarxiv%2Fquant-ph%2F9910078&rft_id=info%3Adoi%2F10.1016%2FS1355-2198%2801%2900034-X&rft_id=info%3Abibcode%2F1999quant.ph.10078P&rft.aulast=Peres&rft.aufirst=Asher&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-Mermin_2017-60"><span class="mw-cite-backlink"><b><a href="#cite_ref-Mermin_2017_60-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMermin2017" class="citation book cs1">Mermin, N. David (2017-01-01). "Why QBism Is Not the Copenhagen Interpretation and What John Bell Might Have Thought of It". In Bertlmann, Reinhold; Zeilinger, Anton (eds.). <i>Quantum [Un]Speakables II</i>. The Frontiers Collection. Springer International Publishing. pp. 83–93. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1409.2454">1409.2454</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-319-38987-5_4">10.1007/978-3-319-38987-5_4</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9783319389851" title="Special:BookSources/9783319389851"><bdi>9783319389851</bdi></a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:118458259">118458259</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Why+QBism+Is+Not+the+Copenhagen+Interpretation+and+What+John+Bell+Might+Have+Thought+of+It&rft.btitle=Quantum+%5BUn%5DSpeakables+II&rft.series=The+Frontiers+Collection&rft.pages=83-93&rft.pub=Springer+International+Publishing&rft.date=2017-01-01&rft_id=info%3Aarxiv%2F1409.2454&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A118458259%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2F978-3-319-38987-5_4&rft.isbn=9783319389851&rft.aulast=Mermin&rft.aufirst=N.+David&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-Bohr1928English-61"><span class="mw-cite-backlink"><b><a href="#cite_ref-Bohr1928English_61-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBohr1928" class="citation journal cs1">Bohr, N. (1928). <a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F121580a0">"The Quantum Postulate and the Recent Development of Atomic Theory"</a>. <i><a href="/wiki/Nature_(journal)" title="Nature (journal)">Nature</a></i>. <b>121</b> (3050): 580–590. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1928Natur.121..580B">1928Natur.121..580B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F121580a0">10.1038/121580a0</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=The+Quantum+Postulate+and+the+Recent+Development+of+Atomic+Theory&rft.volume=121&rft.issue=3050&rft.pages=580-590&rft.date=1928&rft_id=info%3Adoi%2F10.1038%2F121580a0&rft_id=info%3Abibcode%2F1928Natur.121..580B&rft.aulast=Bohr&rft.aufirst=N.&rft_id=https%3A%2F%2Fdoi.org%2F10.1038%252F121580a0&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span> Available in the collection of Bohr's early writings, <i>Atomic Theory and the Description of Nature</i> (1934).</span> </li> <li id="cite_note-Pauling-62"><span class="mw-cite-backlink">^ <a href="#cite_ref-Pauling_62-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Pauling_62-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPauling1960" class="citation book cs1">Pauling, Linus (1960). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/natureofchemical0000paul_3ed"><i>The Nature of the Chemical Bond</i></a></span> (3rd ed.). Itahca, NY: Cornell University Press. p. <a rel="nofollow" class="external text" href="https://archive.org/details/natureofchemical0000paul_3ed/page/47">47</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0801403332" title="Special:BookSources/0801403332"><bdi>0801403332</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">1 March</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Nature+of+the+Chemical+Bond&rft.place=Itahca%2C+NY&rft.pages=47&rft.edition=3rd&rft.pub=Cornell+University+Press&rft.date=1960&rft.isbn=0801403332&rft.aulast=Pauling&rft.aufirst=Linus&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fnatureofchemical0000paul_3ed&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-EB-orbital-63"><span class="mw-cite-backlink"><b><a href="#cite_ref-EB-orbital_63-0">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.britannica.com/EBchecked/topic/431159/orbital">"Orbital (chemistry and physics)", <i>Encyclopædia Britannica </i></a></span> </li> <li id="cite_note-64"><span class="mw-cite-backlink"><b><a href="#cite_ref-64">^</a></b></span> <span class="reference-text">S. Auyang, <i>How is Quantum Field Theory Possible?</i>, Oxford University Press, 1995.</span> </li> <li id="cite_note-65"><span class="mw-cite-backlink"><b><a href="#cite_ref-65">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/davger2.html">The Davisson–Germer experiment, which demonstrates the wave nature of the electron</a></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_quantum_mechanics&action=edit&section=23" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBacciagaluppiValentini2009" class="citation cs2">Bacciagaluppi, Guido; <a href="/wiki/Antony_Valentini" title="Antony Valentini">Valentini, Antony</a> (2009), <i>Quantum theory at the crossroads: reconsidering the 1927 Solvay conference</i>, Cambridge, UK: Cambridge University Press, p. 9184, <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/quant-ph/0609184">quant-ph/0609184</a></span>, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2006quant.ph..9184B">2006quant.ph..9184B</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-81421-8" title="Special:BookSources/978-0-521-81421-8"><bdi>978-0-521-81421-8</bdi></a>, <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/227191829">227191829</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+theory+at+the+crossroads%3A+reconsidering+the+1927+Solvay+conference&rft.place=Cambridge%2C+UK&rft.pages=9184&rft.pub=Cambridge+University+Press&rft.date=2009&rft_id=info%3Aarxiv%2Fquant-ph%2F0609184&rft_id=info%3Aoclcnum%2F227191829&rft_id=info%3Abibcode%2F2006quant.ph..9184B&rft.isbn=978-0-521-81421-8&rft.aulast=Bacciagaluppi&rft.aufirst=Guido&rft.au=Valentini%2C+Antony&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBernstein,_Jeremy2009" class="citation cs2">Bernstein, Jeremy (2009), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=j0Me3brYOL0C"><i>Quantum Leaps</i></a>, Cambridge, Massachusetts: Belknap Press of Harvard University Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-674-03541-6" title="Special:BookSources/978-0-674-03541-6"><bdi>978-0-674-03541-6</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Leaps&rft.place=Cambridge%2C+Massachusetts&rft.pub=Belknap+Press+of+Harvard+University+Press&rft.date=2009&rft.isbn=978-0-674-03541-6&rft.au=Bernstein%2C+Jeremy&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dj0Me3brYOL0C&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></li> <li>Greenberger, Daniel, <a href="/wiki/Klaus_Hentschel" title="Klaus Hentschel">Hentschel, Klaus</a>, Weinert, Friedel (Eds.) <i><a rel="nofollow" class="external text" href="https://www.springer.com/us/book/9783540706229">Compendium of Quantum Physics</a>. Concepts, Experiments, History and Philosophy</i>, New York: Springer, 2009. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-70626-7" title="Special:BookSources/978-3-540-70626-7">978-3-540-70626-7</a>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJammer,_Max1966" class="citation cs2"><a href="/wiki/Max_Jammer" title="Max Jammer">Jammer, Max</a> (1966), <i>The conceptual development of quantum mechanics</i>, New York: McGraw-Hill, <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/534562">534562</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+conceptual+development+of+quantum+mechanics&rft.place=New+York&rft.pub=McGraw-Hill&rft.date=1966&rft_id=info%3Aoclcnum%2F534562&rft.au=Jammer%2C+Max&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJammer,_Max1974" class="citation cs2"><a href="/wiki/Max_Jammer" title="Max Jammer">Jammer, Max</a> (1974), <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/philosophyofquan0000jamm"><i>The philosophy of quantum mechanics: The interpretations of quantum mechanics in historical perspective</i></a></span>, New York: Wiley, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-471-43958-4" title="Special:BookSources/0-471-43958-4"><bdi>0-471-43958-4</bdi></a>, <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/969760">969760</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+philosophy+of+quantum+mechanics%3A+The+interpretations+of+quantum+mechanics+in+historical+perspective&rft.place=New+York&rft.pub=Wiley&rft.date=1974&rft_id=info%3Aoclcnum%2F969760&rft.isbn=0-471-43958-4&rft.au=Jammer%2C+Max&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fphilosophyofquan0000jamm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+quantum+mechanics" class="Z3988"></span></li> <li>A. Whitaker. <i>The New Quantum Age: From Bell's Theorem to Quantum Computation and Teleportation</i>, Oxford University Press, 2011, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-958913-5" title="Special:BookSources/978-0-19-958913-5">978-0-19-958913-5</a></li> <li>Stephen Hawking. <i>The Dreams that Stuff is Made of</i>, Running Press, 2011, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-76-243434-3" title="Special:BookSources/978-0-76-243434-3">978-0-76-243434-3</a></li> <li>A. Douglas Stone. <i>Einstein and the Quantum, the Quest of the Valiant Swabian</i>, Princeton University Press, 2006.</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_quantum_mechanics&action=edit&section=24" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 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abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Quantum_mechanics_topics" title="Template:Quantum mechanics topics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Quantum_mechanics_topics" title="Template talk:Quantum mechanics topics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Quantum_mechanics_topics" title="Special:EditPage/Template:Quantum mechanics topics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Quantum_mechanics" style="font-size:114%;margin:0 4em"><a href="/wiki/Quantum_mechanics" title="Quantum mechanics">Quantum mechanics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Background</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Introduction_to_quantum_mechanics" title="Introduction to quantum mechanics">Introduction</a></li> <li><a class="mw-selflink selflink">History</a> <ul><li><a href="/wiki/Timeline_of_quantum_mechanics" title="Timeline of quantum mechanics">Timeline</a></li></ul></li> <li><a href="/wiki/Classical_mechanics" title="Classical mechanics">Classical mechanics</a></li> <li><a href="/wiki/Old_quantum_theory" title="Old quantum theory">Old quantum theory</a></li> <li><a href="/wiki/Glossary_of_elementary_quantum_mechanics" title="Glossary of elementary quantum mechanics">Glossary</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Fundamentals</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Born_rule" title="Born rule">Born rule</a></li> <li><a href="/wiki/Bra%E2%80%93ket_notation" title="Bra–ket notation">Bra–ket notation</a></li> <li><a href="/wiki/Complementarity_(physics)" title="Complementarity (physics)"> Complementarity</a></li> <li><a href="/wiki/Density_matrix" title="Density matrix">Density matrix</a></li> <li><a href="/wiki/Energy_level" title="Energy level">Energy level</a> <ul><li><a href="/wiki/Ground_state" title="Ground state">Ground state</a></li> <li><a href="/wiki/Excited_state" title="Excited state">Excited state</a></li> <li><a href="/wiki/Degenerate_energy_levels" title="Degenerate energy levels">Degenerate levels</a></li> <li><a href="/wiki/Zero-point_energy" title="Zero-point energy">Zero-point energy</a></li></ul></li> <li><a href="/wiki/Quantum_entanglement" title="Quantum entanglement">Entanglement</a></li> <li><a href="/wiki/Hamiltonian_(quantum_mechanics)" title="Hamiltonian (quantum mechanics)">Hamiltonian</a></li> <li><a href="/wiki/Wave_interference" title="Wave interference">Interference</a></li> <li><a href="/wiki/Quantum_decoherence" title="Quantum decoherence">Decoherence</a></li> <li><a href="/wiki/Measurement_in_quantum_mechanics" title="Measurement in quantum mechanics">Measurement</a></li> <li><a href="/wiki/Quantum_nonlocality" title="Quantum nonlocality">Nonlocality</a></li> <li><a href="/wiki/Quantum_state" title="Quantum state">Quantum state</a></li> <li><a href="/wiki/Quantum_superposition" title="Quantum superposition">Superposition</a></li> <li><a href="/wiki/Quantum_tunnelling" title="Quantum tunnelling">Tunnelling</a></li> <li><a href="/wiki/Scattering_theory" class="mw-redirect" title="Scattering theory">Scattering theory</a></li> <li><a href="/wiki/Symmetry_in_quantum_mechanics" title="Symmetry in quantum mechanics">Symmetry in quantum mechanics</a></li> <li><a href="/wiki/Uncertainty_principle" title="Uncertainty principle">Uncertainty</a></li> <li><a href="/wiki/Wave_function" title="Wave function">Wave function</a> <ul><li><a href="/wiki/Wave_function_collapse" title="Wave function collapse">Collapse</a></li> <li><a href="/wiki/Wave%E2%80%93particle_duality" title="Wave–particle duality">Wave–particle duality</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Formulations</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Mathematical_formulation_of_quantum_mechanics" title="Mathematical formulation of quantum mechanics">Formulations</a></li> <li><a href="/wiki/Heisenberg_picture" title="Heisenberg picture">Heisenberg</a></li> <li><a href="/wiki/Interaction_picture" title="Interaction picture">Interaction</a></li> <li><a href="/wiki/Matrix_mechanics" title="Matrix mechanics">Matrix mechanics</a></li> <li><a href="/wiki/Schr%C3%B6dinger_picture" title="Schrödinger picture">Schrödinger</a></li> <li><a href="/wiki/Path_integral_formulation" title="Path integral formulation">Path integral formulation</a></li> <li><a href="/wiki/Phase-space_formulation" title="Phase-space formulation">Phase space</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Equations</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Klein%E2%80%93Gordon_equation" title="Klein–Gordon equation">Klein–Gordon</a></li> <li><a href="/wiki/Dirac_equation" title="Dirac equation">Dirac</a></li> <li><a href="/wiki/Weyl_equation" title="Weyl equation">Weyl</a></li> <li><a href="/wiki/Majorana_equation" title="Majorana equation">Majorana</a></li> <li><a href="/wiki/Rarita%E2%80%93Schwinger_equation" title="Rarita–Schwinger equation">Rarita–Schwinger</a></li> <li><a href="/wiki/Pauli_equation" title="Pauli equation">Pauli</a></li> <li><a href="/wiki/Rydberg_formula" title="Rydberg formula">Rydberg</a></li> <li><a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Interpretations_of_quantum_mechanics" title="Interpretations of quantum mechanics">Interpretations</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Quantum_Bayesianism" title="Quantum Bayesianism">Bayesian</a></li> <li><a href="/wiki/Consistent_histories" title="Consistent histories">Consistent histories</a></li> <li><a href="/wiki/Copenhagen_interpretation" title="Copenhagen interpretation">Copenhagen</a></li> <li><a href="/wiki/De_Broglie%E2%80%93Bohm_theory" title="De Broglie–Bohm theory">de Broglie–Bohm</a></li> <li><a href="/wiki/Ensemble_interpretation" title="Ensemble interpretation">Ensemble</a></li> <li><a href="/wiki/Hidden-variable_theory" title="Hidden-variable theory">Hidden-variable</a> <ul><li><a href="/wiki/Local_hidden-variable_theory" title="Local hidden-variable theory">Local</a> <ul><li><a href="/wiki/Superdeterminism" title="Superdeterminism">Superdeterminism</a></li></ul></li></ul></li> <li><a href="/wiki/Many-worlds_interpretation" title="Many-worlds interpretation">Many-worlds</a></li> <li><a href="/wiki/Objective-collapse_theory" title="Objective-collapse theory">Objective collapse</a></li> <li><a href="/wiki/Quantum_logic" title="Quantum logic">Quantum logic</a></li> <li><a href="/wiki/Relational_quantum_mechanics" title="Relational quantum mechanics">Relational</a></li> <li><a href="/wiki/Transactional_interpretation" title="Transactional interpretation">Transactional</a></li> <li><a href="/wiki/Von_Neumann%E2%80%93Wigner_interpretation" title="Von Neumann–Wigner interpretation">Von Neumann–Wigner</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Experiments</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bell_test" title="Bell test">Bell test</a></li> <li><a href="/wiki/Davisson%E2%80%93Germer_experiment" title="Davisson–Germer experiment">Davisson–Germer</a></li> <li><a href="/wiki/Delayed-choice_quantum_eraser" title="Delayed-choice quantum eraser">Delayed-choice quantum eraser</a></li> <li><a href="/wiki/Double-slit_experiment" title="Double-slit experiment">Double-slit</a></li> <li><a href="/wiki/Franck%E2%80%93Hertz_experiment" title="Franck–Hertz experiment">Franck–Hertz</a></li> <li><a href="/wiki/Mach%E2%80%93Zehnder_interferometer" title="Mach–Zehnder interferometer">Mach–Zehnder interferometer</a></li> <li><a href="/wiki/Elitzur%E2%80%93Vaidman_bomb_tester" title="Elitzur–Vaidman bomb tester">Elitzur–Vaidman</a></li> <li><a href="/wiki/Popper%27s_experiment" title="Popper's experiment">Popper</a></li> <li><a href="/wiki/Quantum_eraser_experiment" title="Quantum eraser experiment">Quantum eraser</a></li> <li><a href="/wiki/Stern%E2%80%93Gerlach_experiment" title="Stern–Gerlach experiment">Stern–Gerlach</a></li> <li><a href="/wiki/Wheeler%27s_delayed-choice_experiment" title="Wheeler's delayed-choice experiment">Wheeler's delayed choice</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Quantum_nanoscience" class="mw-redirect" title="Quantum nanoscience">Science</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Quantum_biology" title="Quantum biology">Quantum biology</a></li> <li><a href="/wiki/Quantum_chemistry" title="Quantum chemistry">Quantum chemistry</a></li> <li><a href="/wiki/Quantum_chaos" title="Quantum chaos">Quantum chaos</a></li> <li><a href="/wiki/Quantum_cosmology" title="Quantum cosmology">Quantum cosmology</a></li> <li><a href="/wiki/Quantum_differential_calculus" title="Quantum differential calculus">Quantum differential calculus</a></li> <li><a href="/wiki/Quantum_dynamics" title="Quantum dynamics">Quantum dynamics</a></li> <li><a href="/wiki/Quantum_geometry" title="Quantum geometry">Quantum geometry</a></li> <li><a href="/wiki/Measurement_problem" title="Measurement problem">Quantum measurement problem</a></li> <li><a href="/wiki/Quantum_mind" title="Quantum mind">Quantum mind</a></li> <li><a href="/wiki/Quantum_stochastic_calculus" title="Quantum stochastic calculus">Quantum stochastic calculus</a></li> <li><a href="/wiki/Quantum_spacetime" title="Quantum spacetime">Quantum spacetime</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Quantum_technology" class="mw-redirect" title="Quantum technology">Technology</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Quantum_algorithm" title="Quantum algorithm">Quantum algorithms</a></li> <li><a href="/wiki/Quantum_amplifier" title="Quantum amplifier">Quantum amplifier</a></li> <li><a href="/wiki/Quantum_bus" title="Quantum bus">Quantum bus</a></li> <li><a href="/wiki/Quantum_cellular_automaton" title="Quantum cellular automaton">Quantum cellular automata</a> <ul><li><a href="/wiki/Quantum_finite_automaton" title="Quantum finite automaton">Quantum finite automata</a></li></ul></li> <li><a href="/wiki/Quantum_channel" title="Quantum channel">Quantum channel</a></li> <li><a href="/wiki/Quantum_circuit" title="Quantum circuit">Quantum circuit</a></li> <li><a href="/wiki/Quantum_complexity_theory" title="Quantum complexity theory">Quantum complexity theory</a></li> <li><a href="/wiki/Quantum_computing" title="Quantum computing">Quantum computing</a> <ul><li><a href="/wiki/Timeline_of_quantum_computing_and_communication" title="Timeline of quantum computing and communication">Timeline</a></li></ul></li> <li><a href="/wiki/Quantum_cryptography" title="Quantum cryptography">Quantum cryptography</a></li> <li><a href="/wiki/Quantum_electronics" class="mw-redirect" title="Quantum electronics">Quantum electronics</a></li> <li><a href="/wiki/Quantum_error_correction" title="Quantum error correction">Quantum error correction</a></li> <li><a href="/wiki/Quantum_imaging" title="Quantum imaging">Quantum imaging</a></li> <li><a href="/wiki/Quantum_image_processing" title="Quantum image processing">Quantum image processing</a></li> <li><a href="/wiki/Quantum_information" title="Quantum information">Quantum information</a></li> <li><a href="/wiki/Quantum_key_distribution" title="Quantum key distribution">Quantum key distribution</a></li> <li><a href="/wiki/Quantum_logic" title="Quantum logic">Quantum logic</a></li> <li><a href="/wiki/Quantum_logic_gate" title="Quantum logic gate">Quantum logic gates</a></li> <li><a href="/wiki/Quantum_machine" title="Quantum machine">Quantum machine</a></li> <li><a href="/wiki/Quantum_machine_learning" title="Quantum machine learning">Quantum machine learning</a></li> <li><a href="/wiki/Quantum_metamaterial" title="Quantum metamaterial">Quantum metamaterial</a></li> <li><a href="/wiki/Quantum_metrology" title="Quantum metrology">Quantum metrology</a></li> <li><a href="/wiki/Quantum_network" title="Quantum network">Quantum network</a></li> <li><a href="/wiki/Quantum_neural_network" title="Quantum neural network">Quantum neural network</a></li> <li><a href="/wiki/Quantum_optics" title="Quantum optics">Quantum optics</a></li> <li><a href="/wiki/Quantum_programming" title="Quantum programming">Quantum programming</a></li> <li><a href="/wiki/Quantum_sensor" title="Quantum sensor">Quantum sensing</a></li> <li><a href="/wiki/Quantum_simulator" title="Quantum simulator">Quantum simulator</a></li> <li><a href="/wiki/Quantum_teleportation" title="Quantum teleportation">Quantum teleportation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Extensions</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Quantum_fluctuation" title="Quantum fluctuation">Quantum fluctuation</a></li> <li><a href="/wiki/Casimir_effect" title="Casimir effect">Casimir effect</a></li> <li><a href="/wiki/Quantum_statistical_mechanics" title="Quantum statistical mechanics">Quantum statistical mechanics</a></li> <li><a href="/wiki/Quantum_field_theory" title="Quantum field theory">Quantum field theory</a> <ul><li><a href="/wiki/History_of_quantum_field_theory" title="History of quantum field theory">History</a></li></ul></li> <li><a href="/wiki/Quantum_gravity" title="Quantum gravity">Quantum gravity</a></li> <li><a href="/wiki/Relativistic_quantum_mechanics" title="Relativistic quantum mechanics">Relativistic quantum mechanics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Schr%C3%B6dinger%27s_cat" title="Schrödinger's cat">Schrödinger's cat</a> <ul><li><a href="/wiki/Schr%C3%B6dinger%27s_cat_in_popular_culture" title="Schrödinger's cat in popular culture">in popular culture</a></li></ul></li> <li><a href="/wiki/Wigner%27s_friend" title="Wigner's friend">Wigner's friend</a></li> <li><a href="/wiki/Einstein%E2%80%93Podolsky%E2%80%93Rosen_paradox" title="Einstein–Podolsky–Rosen paradox">EPR paradox</a></li> <li><a href="/wiki/Quantum_mysticism" title="Quantum mysticism">Quantum mysticism</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Quantum_mechanics" title="Category:Quantum mechanics">Category</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="History_of_physics_(timeline)" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:History_of_physics" title="Template:History of physics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:History_of_physics" title="Template talk:History of physics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:History_of_physics" title="Special:EditPage/Template:History of physics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="History_of_physics_(timeline)" style="font-size:114%;margin:0 4em"><a href="/wiki/History_of_physics" title="History of physics">History of physics</a> (<a href="/wiki/Timeline_of_fundamental_physics_discoveries" title="Timeline of fundamental physics discoveries">timeline</a>)</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Classical_physics" title="Classical physics">Classical physics</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/History_of_astronomy" title="History of astronomy">Astronomy</a> <ul><li><a href="/wiki/Timeline_of_astronomy" title="Timeline of astronomy">timeline</a></li></ul></li> <li><a href="/wiki/History_of_electromagnetic_theory" title="History of electromagnetic theory">Electromagnetism</a> <ul><li><a href="/wiki/Timeline_of_electromagnetism_and_classical_optics" title="Timeline of electromagnetism and classical optics">timeline</a></li> <li><a href="/wiki/History_of_electrical_engineering" title="History of electrical engineering">Electrical engineering</a></li> <li><a href="/wiki/History_of_Maxwell%27s_equations" title="History of Maxwell's equations">Maxwell's equations</a></li></ul></li> <li><a href="/wiki/History_of_fluid_mechanics" title="History of fluid mechanics">Fluid mechanics</a> <ul><li><a href="/wiki/Timeline_of_fluid_and_continuum_mechanics" title="Timeline of fluid and continuum mechanics">timeline</a></li> <li><a href="/wiki/History_of_aerodynamics" title="History of aerodynamics">Aerodynamics</a></li></ul></li> <li><a href="/wiki/History_of_classical_field_theory" title="History of classical field theory">Field theory</a></li> <li><a href="/wiki/History_of_gravitational_theory" title="History of gravitational theory">Gravitational theory</a> <ul><li><a href="/wiki/Timeline_of_gravitational_physics_and_relativity" title="Timeline of gravitational physics and relativity">timeline</a></li></ul></li> <li><a href="/wiki/History_of_materials_science" title="History of materials science">Material science</a> <ul><li><a href="/wiki/Timeline_of_materials_technology" title="Timeline of materials technology">timeline</a></li> <li><a href="/wiki/History_of_metamaterials" title="History of metamaterials">Metamaterials</a></li></ul></li> <li><a href="/wiki/History_of_classical_mechanics" title="History of classical mechanics">Mechanics</a> <ul><li><a href="/wiki/Timeline_of_classical_mechanics" title="Timeline of classical mechanics">timeline</a></li> <li><a href="/wiki/History_of_variational_principles_in_physics" title="History of variational principles in physics">Variational principles</a></li></ul></li> <li><a href="/wiki/History_of_optics" title="History of optics">Optics</a> <ul><li><a href="/wiki/History_of_spectroscopy" title="History of spectroscopy">Spectroscopy</a></li></ul></li> <li><a href="/wiki/History_of_thermodynamics" title="History of thermodynamics">Thermodynamics</a> <ul><li><a href="/wiki/Timeline_of_thermodynamics" title="Timeline of thermodynamics">timeline</a></li> <li><a href="/wiki/History_of_energy" title="History of energy">Energy</a></li> <li><a href="/wiki/History_of_entropy" title="History of entropy">Entropy</a></li> <li><a href="/wiki/History_of_perpetual_motion_machines" title="History of perpetual motion machines">Perpetual motion</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Modern_physics" title="Modern physics">Modern physics</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Computational physics <ul><li><a href="/wiki/Timeline_of_computational_physics" title="Timeline of computational physics">timeline</a></li></ul></li> <li>Condensed matter <ul><li><a href="/wiki/Timeline_of_condensed_matter_physics" title="Timeline of condensed matter physics">timeline</a></li> <li><a href="/wiki/History_of_superconductivity" title="History of superconductivity">Superconductivity</a></li></ul></li> <li>Cosmology <ul><li><a href="/wiki/Timeline_of_cosmological_theories" title="Timeline of cosmological theories">timeline</a></li> <li><a href="/wiki/History_of_the_Big_Bang_theory" title="History of the Big Bang theory">Big Bang theory</a></li></ul></li> <li><a href="/wiki/History_of_general_relativity" title="History of general relativity">General relativity</a> <ul><li><a href="/wiki/Tests_of_general_relativity" title="Tests of general relativity">tests</a></li></ul></li> <li><a href="/wiki/History_of_geophysics" title="History of geophysics">Geophysics</a></li> <li>Nuclear physics <ul><li><a href="/wiki/Discovery_of_nuclear_fission" title="Discovery of nuclear fission">Fission</a></li> <li><a href="/wiki/History_of_nuclear_fusion" title="History of nuclear fusion">Fusion</a></li> <li><a href="/wiki/History_of_nuclear_power" title="History of nuclear power">Power</a></li> <li><a href="/wiki/History_of_nuclear_weapons" title="History of nuclear weapons">Weapons</a></li></ul></li> <li><a class="mw-selflink selflink">Quantum mechanics</a> <ul><li><a href="/wiki/Timeline_of_quantum_mechanics" title="Timeline of quantum mechanics">timeline</a></li> <li><a href="/wiki/History_of_atomic_theory" title="History of atomic theory">Atoms</a></li> <li><a href="/wiki/History_of_molecular_theory" title="History of molecular theory">Molecules</a></li> <li><a href="/wiki/History_of_quantum_field_theory" title="History of quantum field theory">Quantum field theory</a></li></ul></li> <li><a href="/wiki/History_of_subatomic_physics" title="History of subatomic physics">Subatomic physics</a> <ul><li><a href="/wiki/Timeline_of_atomic_and_subatomic_physics" title="Timeline of atomic and subatomic physics">timeline</a></li></ul></li> <li><a href="/wiki/History_of_special_relativity" title="History of special relativity">Special relativity</a> <ul><li><a href="/wiki/Timeline_of_special_relativity_and_the_speed_of_light" title="Timeline of special relativity and the speed of light">timeline</a></li> <li><a href="/wiki/History_of_Lorentz_transformations" title="History of Lorentz transformations">Lorentz transformations</a></li> <li><a href="/wiki/Tests_of_special_relativity" title="Tests of special relativity">tests</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Recent developments</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Quantum information <ul><li><a href="/wiki/Timeline_of_quantum_computing_and_communication" title="Timeline of quantum computing and communication">timeline</a></li></ul></li> <li><a href="/wiki/History_of_loop_quantum_gravity" title="History of loop quantum gravity">Loop quantum gravity</a></li> <li><a href="/wiki/History_of_nanotechnology" title="History of nanotechnology">Nanotechnology</a></li> <li><a href="/wiki/History_of_string_theory" title="History of string theory">String theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">On specific discoveries</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Discovery_of_cosmic_microwave_background_radiation" title="Discovery of cosmic microwave background radiation">Cosmic microwave background</a></li> <li><a href="/wiki/Discovery_of_graphene" title="Discovery of graphene">Graphene</a></li> <li><a href="/wiki/First_observation_of_gravitational_waves" title="First observation of gravitational waves">Gravitational waves</a></li> <li>Subatomic particles <ul><li><a href="/wiki/Timeline_of_particle_discoveries" title="Timeline of particle discoveries">timeline</a></li> <li><a href="/wiki/Search_for_the_Higgs_boson" title="Search for the Higgs boson">Higgs boson</a></li> <li><a href="/wiki/Discovery_of_the_neutron" title="Discovery of the neutron">Neutron</a></li></ul></li> <li><a href="/wiki/R%C3%B8mer%27s_determination_of_the_speed_of_light" title="Rømer's determination of the speed of light">Speed of light</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By periods</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Copernican_Revolution" title="Copernican Revolution">Copernican Revolution</a></li> <li><a href="/wiki/Golden_age_of_physics" title="Golden age of physics">Golden age of physics</a></li> <li><a href="/wiki/Golden_age_of_cosmology" title="Golden age of cosmology">Golden age of cosmology</a></li> <li><a href="/wiki/Physics_in_the_medieval_Islamic_world" title="Physics in the medieval Islamic world">Medieval Islamic world</a> <ul><li><a href="/wiki/Astronomy_in_the_medieval_Islamic_world" title="Astronomy in the medieval Islamic world">Astronomy</a></li></ul></li> <li><a href="/wiki/Noisy_intermediate-scale_quantum_era" title="Noisy intermediate-scale quantum era">Noisy intermediate-scale quantum era</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By groups</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Harvard_Computers" title="Harvard Computers">Harvard Computers</a></li> <li><a href="/wiki/The_Martians_(scientists)" title="The Martians (scientists)">The Martians</a></li> <li><a href="/wiki/Oxford_Calculators" title="Oxford Calculators">Oxford Calculators</a></li> <li><a href="/wiki/Via_Panisperna_boys" title="Via Panisperna boys">Via Panisperna boys</a></li> <li><a href="/wiki/Women_in_physics" title="Women in physics">Women in physics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Scientific disputes</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bohr%E2%80%93Einstein_debates" title="Bohr–Einstein debates">Bohr–Einstein</a></li> <li><a href="/wiki/Chandrasekhar%E2%80%93Eddington_dispute" title="Chandrasekhar–Eddington dispute">Chandrasekhar–Eddington</a></li> <li><a href="/wiki/Galileo_affair" title="Galileo affair">Galileo affair</a></li> <li><a href="/wiki/Leibniz%E2%80%93Newton_calculus_controversy" title="Leibniz–Newton calculus controversy">Leibniz–Newton</a></li> <li><a href="/wiki/Mechanical_equivalent_of_heat" title="Mechanical equivalent of heat">Joule–von Mayer</a></li> <li><a href="/wiki/Great_Debate_(astronomy)" title="Great Debate (astronomy)">Shapley–Curtis</a></li> <li>Relativity priority <ul><li><a href="/wiki/Relativity_priority_dispute" title="Relativity priority dispute">Special relativity</a></li> <li><a href="/wiki/General_relativity_priority_dispute" title="General relativity priority dispute">General relativity</a></li></ul></li> <li><a href="/wiki/Transfermium_Wars" title="Transfermium Wars">Transfermium Wars</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:History_of_physics" title="Category:History of physics">Category</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" 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