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<li id="toc-Evidence_of_quanta_from_the_photoelectric_effect" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Evidence_of_quanta_from_the_photoelectric_effect"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Evidence of quanta from the photoelectric effect</span> </div> </a> <ul id="toc-Evidence_of_quanta_from_the_photoelectric_effect-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quantization_of_bound_electrons_in_atoms" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Quantization_of_bound_electrons_in_atoms"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Quantization of bound electrons in atoms</span> </div> </a> <ul id="toc-Quantization_of_bound_electrons_in_atoms-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quantization_of_spin" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Quantization_of_spin"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Quantization of spin</span> </div> </a> <ul id="toc-Quantization_of_spin-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quantization_of_matter" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Quantization_of_matter"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Quantization of matter</span> </div> </a> <ul id="toc-Quantization_of_matter-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_developments" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Further_developments"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.5</span> <span>Further developments</span> </div> </a> <ul id="toc-Further_developments-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quantum_radiation,_quantum_fields" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Quantum_radiation,_quantum_fields"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.6</span> <span>Quantum radiation, quantum fields</span> </div> </a> <ul id="toc-Quantum_radiation,_quantum_fields-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Wave–particle_duality" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Wave–particle_duality"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Wave–particle duality</span> </div> </a> <ul id="toc-Wave–particle_duality-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Uncertainty_principle" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Uncertainty_principle"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Uncertainty principle</span> </div> </a> <ul id="toc-Uncertainty_principle-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Wave_function_collapse" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Wave_function_collapse"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Wave function collapse</span> </div> </a> <ul id="toc-Wave_function_collapse-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Eigenstates_and_eigenvalues" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Eigenstates_and_eigenvalues"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Eigenstates and eigenvalues</span> </div> </a> <ul id="toc-Eigenstates_and_eigenvalues-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-The_Pauli_exclusion_principle" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#The_Pauli_exclusion_principle"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>The Pauli exclusion principle</span> </div> </a> <ul id="toc-The_Pauli_exclusion_principle-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dirac_wave_equation" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Dirac_wave_equation"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Dirac wave equation</span> </div> </a> <ul id="toc-Dirac_wave_equation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quantum_entanglement" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Quantum_entanglement"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Quantum entanglement</span> </div> </a> <ul id="toc-Quantum_entanglement-sublist" class="vector-toc-list"> </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">9</span> <span>Quantum field theory</span> </div> </a> <button aria-controls="toc-Quantum_field_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 Quantum field theory subsection</span> </button> <ul id="toc-Quantum_field_theory-sublist" class="vector-toc-list"> <li id="toc-Quantum_electrodynamics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Quantum_electrodynamics"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.1</span> <span>Quantum electrodynamics</span> </div> </a> <ul id="toc-Quantum_electrodynamics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Standard_Model" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Standard_Model"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.2</span> <span>Standard Model</span> </div> </a> <ul id="toc-Standard_Model-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Interpretations" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Interpretations"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Interpretations</span> </div> </a> <ul id="toc-Interpretations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Applications" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Applications</span> </div> </a> <button aria-controls="toc-Applications-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 Applications subsection</span> </button> <ul id="toc-Applications-sublist" class="vector-toc-list"> <li id="toc-Everyday_applications" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Everyday_applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">11.1</span> <span>Everyday applications</span> </div> </a> <ul id="toc-Everyday_applications-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Technological_applications" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Technological_applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">11.2</span> <span>Technological applications</span> </div> </a> <ul id="toc-Technological_applications-sublist" class="vector-toc-list"> </ul> </li> </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">12</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-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">14</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliography" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliography"> <div class="vector-toc-text"> <span class="vector-toc-numb">15</span> <span>Bibliography</span> </div> </a> <ul id="toc-Bibliography-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">16</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">17</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" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Introduction to quantum mechanics</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 21 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-21" 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">21 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/%D9%85%D9%82%D8%AF%D9%85%D8%A9_%D9%81%D9%8A_%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="مقدمة في ميكانيكا الكم – Arabic" lang="ar" hreflang="ar" data-title="مقدمة في 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%A6%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%B0_%E0%A6%AD%E0%A7%82%E0%A6%AE%E0%A6%BF%E0%A6%95%E0%A6%BE" title="কোয়ান্টাম বলবিদ্যার ভূমিকা – Bangla" lang="bn" hreflang="bn" data-title="কোয়ান্টাম বলবিদ্যার ভূমিকা" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Introduction_%C3%A0_la_m%C3%A9canique_quantique" title="Introduction à la mécanique quantique – French" lang="fr" hreflang="fr" data-title="Introduction à 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_%EA%B0%9C%EB%A1%A0" title="양자역학 개론 – Korean" lang="ko" hreflang="ko" data-title="양자역학 개론" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%B5%E0%A4%BE%E0%A4%82%E0%A4%9F%E0%A4%AE_%E0%A4%AF%E0%A4%BE%E0%A4%82%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%95%E0%A5%80_%E0%A4%95%E0%A4%BE_%E0%A4%AA%E0%A4%B0%E0%A4%BF%E0%A4%9A%E0%A4%AF" title="क्वांटम यांत्रिकी का परिचय – Hindi" lang="hi" hreflang="hi" data-title="क्वांटम यांत्रिकी का परिचय" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Uvod_u_kvantnu_mehaniku" title="Uvod u kvantnu mehaniku – Croatian" lang="hr" hreflang="hr" data-title="Uvod u kvantnu mehaniku" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Pengantar_mekanika_kuantum" title="Pengantar mekanika kuantum – Indonesian" lang="id" hreflang="id" data-title="Pengantar mekanika kuantum" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Inngangur_a%C3%B0_skammtafr%C3%A6%C3%B0i" title="Inngangur að skammtafræði – Icelandic" lang="is" hreflang="is" data-title="Inngangur að skammtafræði" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%95%E0%B3%8D%E0%B2%B5%E0%B2%BE%E0%B2%82%E0%B2%9F%E0%B2%AE%E0%B3%8D_%E0%B2%AE%E0%B3%86%E0%B2%95%E0%B3%8D%E0%B2%AF%E0%B2%BE%E0%B2%A8%E0%B2%BF%E0%B2%95%E0%B3%8D%E0%B2%B8%E0%B3%8D" title="ಕ್ವಾಂಟಮ್ ಮೆಕ್ಯಾನಿಕ್ಸ್ – Kannada" lang="kn" hreflang="kn" data-title="ಕ್ವಾಂಟಮ್ ಮೆಕ್ಯಾನಿಕ್ಸ್" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AA%E0%A5%81%E0%A4%82%E0%A4%9C_%E0%A4%AF%E0%A4%BE%E0%A4%AE%E0%A4%BF%E0%A4%95%E0%A4%BE%E0%A4%9A%E0%A5%80_%E0%A4%93%E0%A4%B3%E0%A4%96" title="पुंज यामिकाची ओळख – Marathi" lang="mr" hreflang="mr" data-title="पुंज यामिकाची ओळख" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Pengenalan_pada_mekanik_kuantum" title="Pengenalan pada mekanik kuantum – Malay" lang="ms" hreflang="ms" data-title="Pengenalan pada mekanik kuantum" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</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%A8%E0%A8%BE%E0%A8%B2_%E0%A8%9C%E0%A8%BE%E0%A8%A3-%E0%A8%AA%E0%A8%9B%E0%A8%BE%E0%A8%A3" title="ਕੁਆਂਟਮ ਮਕੈਨਿਕਸ ਨਾਲ ਜਾਣ-ਪਛਾਣ – Punjabi" lang="pa" hreflang="pa" data-title="ਕੁਆਂਟਮ ਮਕੈਨਿਕਸ ਨਾਲ ਜਾਣ-ਪਛਾਣ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%DA%A9%D9%88%D8%A7%D9%86%D9%B9%D9%85_%D9%85%DA%A9%DB%8C%D9%86%DA%A9%D8%B3_%D9%86%D8%A7%D9%84_%D8%AC%D8%A7%D9%86-%D9%BE%DA%86%DA%BE%D8%A7%D9%86" title="کوانٹم مکینکس نال جان-پچھان – Western Punjabi" lang="pnb" hreflang="pnb" data-title="کوانٹم مکینکس نال جان-پچھان" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Introdu%C3%A7%C3%A3o_%C3%A0_mec%C3%A2nica_qu%C3%A2ntica" title="Introdução à mecânica quântica – Portuguese" lang="pt" hreflang="pt" data-title="Introdução à mecânica quântica" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Introducere_%C3%AEn_mecanica_cuantic%C4%83" title="Introducere în mecanica cuantică – Romanian" lang="ro" hreflang="ro" data-title="Introducere în mecanica cuantică" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/%C3%9Avod_do_kvantovej_mechaniky" title="Úvod do kvantovej mechaniky – Slovak" lang="sk" hreflang="sk" data-title="Úvod do kvantovej mechaniky" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Uvod_v_kvantno_mehaniko" title="Uvod v kvantno mehaniko – Slovenian" lang="sl" hreflang="sl" data-title="Uvod v kvantno mehaniko" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%9A%E0%B8%97%E0%B8%99%E0%B8%B3%E0%B8%81%E0%B8%A5%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C%E0%B8%84%E0%B8%A7%E0%B8%AD%E0%B8%99%E0%B8%95%E0%B8%B1%E0%B8%A1" title="บทนำกลศาสตร์ควอนตัม – Thai" lang="th" hreflang="th" data-title="บทนำกลศาสตร์ควอนตัม" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Kuantum_mekani%C4%9Fine_giri%C5%9F" title="Kuantum mekaniğine giriş – Turkish" lang="tr" hreflang="tr" data-title="Kuantum mekaniğine giriş" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk 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class="mw-redirectedfrom">(Redirected from <a href="/w/index.php?title=Basic_quantum_mechanics&redirect=no" class="mw-redirect" title="Basic quantum mechanics">Basic quantum mechanics</a>)</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Non-mathematical introduction</div> <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">For the book by David J. Griffiths, see <a href="/wiki/Introduction_to_Quantum_Mechanics_(book)" title="Introduction to Quantum Mechanics (book)">Introduction to Quantum Mechanics (book)</a>.</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">This article is a non-technical introduction to the subject. 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rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist nowraplinks" style="width:19.0em;"><tbody><tr><td class="sidebar-pretitle">Part of a series of articles about</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="/wiki/Quantum_mechanics" title="Quantum mechanics">Quantum mechanics</a></th></tr><tr><td class="sidebar-image"><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 i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi mathvariant="normal">Ψ</mi> <mo fence="false" stretchy="false">⟩</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi mathvariant="normal">Ψ</mi> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1799e4a910c7d26396922a20ef5ceec25ca1871c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:16.882ex; height:5.509ex;" alt="{\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle }"></span><div class="sidebar-caption" style="font-size:90%;padding-top:0.4em;font-style:italic;"><a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger equation</a></div></td></tr><tr><td class="sidebar-above hlist nowrap" style="display:block;margin-bottom:0.4em;"> <ul><li><a class="mw-selflink selflink">Introduction</a></li> <li><a href="/wiki/Glossary_of_elementary_quantum_mechanics" title="Glossary of elementary quantum mechanics">Glossary</a></li> <li><a href="/wiki/History_of_quantum_mechanics" title="History of quantum mechanics">History</a></li></ul></td></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)">Background</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"> <ul><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/Bra%E2%80%93ket_notation" title="Bra–ket notation">Bra–ket notation</a></li></ul> <div class="hlist"> <ul><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></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)">Fundamentals</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"><div class="hlist"> <ul><li><a href="/wiki/Complementarity_(physics)" title="Complementarity (physics)">Complementarity</a></li> <li><a href="/wiki/Quantum_decoherence" title="Quantum decoherence">Decoherence</a></li> <li><a href="/wiki/Quantum_entanglement" title="Quantum entanglement">Entanglement</a></li> <li><a href="/wiki/Energy_level" title="Energy level">Energy level</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_number" title="Quantum number">Quantum number</a></li> <li><a href="/wiki/Quantum_state" title="Quantum state">State</a></li> <li><a href="/wiki/Quantum_superposition" title="Quantum superposition">Superposition</a></li> <li><a href="/wiki/Symmetry_in_quantum_mechanics" title="Symmetry in quantum mechanics">Symmetry</a></li> <li><a href="/wiki/Quantum_tunnelling" title="Quantum tunnelling">Tunnelling</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></ul></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)">Experiments</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"><div class="hlist"> <ul><li><a href="/wiki/Bell_test" title="Bell test">Bell's inequality</a></li> <li><a href="/wiki/CHSH_inequality" title="CHSH inequality">CHSH inequality</a></li> <li><a href="/wiki/Davisson%E2%80%93Germer_experiment" title="Davisson–Germer experiment">Davisson–Germer</a></li> <li><a href="/wiki/Double-slit_experiment" title="Double-slit experiment">Double-slit</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/Franck%E2%80%93Hertz_experiment" title="Franck–Hertz experiment">Franck–Hertz</a></li> <li><a href="/wiki/Leggett_inequality" title="Leggett inequality">Leggett inequality</a></li> <li><a href="/wiki/Leggett%E2%80%93Garg_inequality" title="Leggett–Garg inequality">Leggett–Garg inequality</a></li> <li><a href="/wiki/Mach%E2%80%93Zehnder_interferometer" title="Mach–Zehnder interferometer">Mach–Zehnder</a></li> <li><a href="/wiki/Popper%27s_experiment" title="Popper's experiment">Popper</a></li></ul> </div> <ul><li><a href="/wiki/Quantum_eraser_experiment" title="Quantum eraser experiment">Quantum eraser</a> <ul><li><a href="/wiki/Delayed-choice_quantum_eraser" title="Delayed-choice quantum eraser">Delayed-choice</a></li></ul></li></ul> <div class="hlist"> <ul><li><a href="/wiki/Schr%C3%B6dinger%27s_cat" title="Schrödinger's cat">Schrödinger's cat</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></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)">Formulations</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"> <ul><li><a href="/wiki/Mathematical_formulation_of_quantum_mechanics" title="Mathematical formulation of quantum mechanics">Overview</a></li></ul> <div class="hlist"> <ul><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</a></li> <li><a href="/wiki/Phase-space_formulation" title="Phase-space formulation">Phase-space</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">Sum-over-histories (path integral)</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)">Equations</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"><div class="hlist"> <ul><li><a href="/wiki/Dirac_equation" title="Dirac equation">Dirac</a></li> <li><a href="/wiki/Klein%E2%80%93Gordon_equation" title="Klein–Gordon equation">Klein–Gordon</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></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)"><a href="/wiki/Interpretations_of_quantum_mechanics" title="Interpretations of quantum mechanics">Interpretations</a></div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"><div class="hlist"> <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></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)">Advanced topics</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"> <ul><li><a href="/wiki/Relativistic_quantum_mechanics" title="Relativistic quantum mechanics">Relativistic quantum mechanics</a></li> <li><a href="/wiki/Quantum_field_theory" title="Quantum field theory">Quantum field theory</a></li> <li><a href="/wiki/Quantum_information_science" title="Quantum information science">Quantum information science</a></li> <li><a href="/wiki/Quantum_computing" title="Quantum computing">Quantum computing</a></li> <li><a href="/wiki/Quantum_chaos" title="Quantum chaos">Quantum chaos</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/Density_matrix" title="Density matrix">Density matrix</a></li> <li><a href="/wiki/Scattering_theory" class="mw-redirect" title="Scattering theory">Scattering theory</a></li> <li><a href="/wiki/Quantum_statistical_mechanics" title="Quantum statistical mechanics">Quantum statistical mechanics</a></li> <li><a href="/wiki/Quantum_machine_learning" title="Quantum machine learning">Quantum machine learning</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"><div class="hlist"> <ul><li><a href="/wiki/Yakir_Aharonov" title="Yakir Aharonov">Aharonov</a></li> <li><a href="/wiki/John_Stewart_Bell" title="John Stewart Bell">Bell</a></li> <li><a href="/wiki/Hans_Bethe" title="Hans Bethe">Bethe</a></li> <li><a href="/wiki/Patrick_Blackett" title="Patrick Blackett">Blackett</a></li> <li><a href="/wiki/Felix_Bloch" title="Felix Bloch">Bloch</a></li> <li><a href="/wiki/David_Bohm" title="David Bohm">Bohm</a></li> <li><a href="/wiki/Niels_Bohr" title="Niels Bohr">Bohr</a></li> <li><a href="/wiki/Max_Born" title="Max Born">Born</a></li> <li><a href="/wiki/Satyendra_Nath_Bose" title="Satyendra Nath Bose">Bose</a></li> <li><a href="/wiki/Louis_de_Broglie" title="Louis de Broglie">de Broglie</a></li> <li><a href="/wiki/Arthur_Compton" title="Arthur Compton">Compton</a></li> <li><a href="/wiki/Paul_Dirac" title="Paul Dirac">Dirac</a></li> <li><a href="/wiki/Clinton_Davisson" title="Clinton Davisson">Davisson</a></li> <li><a href="/wiki/Peter_Debye" title="Peter Debye">Debye</a></li> <li><a href="/wiki/Paul_Ehrenfest" title="Paul Ehrenfest">Ehrenfest</a></li> <li><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a></li> <li><a href="/wiki/Hugh_Everett_III" title="Hugh Everett III">Everett</a></li> <li><a href="/wiki/Vladimir_Fock" title="Vladimir Fock">Fock</a></li> <li><a href="/wiki/Enrico_Fermi" title="Enrico Fermi">Fermi</a></li> <li><a href="/wiki/Richard_Feynman" title="Richard Feynman">Feynman</a></li> <li><a href="/wiki/Roy_J._Glauber" title="Roy J. Glauber">Glauber</a></li> <li><a href="/wiki/Martin_Gutzwiller" title="Martin Gutzwiller">Gutzwiller</a></li> <li><a href="/wiki/Werner_Heisenberg" title="Werner Heisenberg">Heisenberg</a></li> <li><a href="/wiki/David_Hilbert" title="David Hilbert">Hilbert</a></li> <li><a href="/wiki/Pascual_Jordan" title="Pascual Jordan">Jordan</a></li> <li><a href="/wiki/Hans_Kramers" title="Hans Kramers">Kramers</a></li> <li><a href="/wiki/Willis_Lamb" title="Willis Lamb">Lamb</a></li> <li><a href="/wiki/Lev_Landau" title="Lev Landau">Landau</a></li> <li><a href="/wiki/Max_von_Laue" title="Max von Laue">Laue</a></li> <li><a href="/wiki/Henry_Moseley" title="Henry Moseley">Moseley</a></li> <li><a href="/wiki/Robert_Andrews_Millikan" title="Robert Andrews Millikan">Millikan</a></li> <li><a href="/wiki/Heike_Kamerlingh_Onnes" title="Heike Kamerlingh Onnes">Onnes</a></li> <li><a href="/wiki/Wolfgang_Pauli" title="Wolfgang Pauli">Pauli</a></li> <li><a href="/wiki/Max_Planck" title="Max Planck">Planck</a></li> <li><a href="/wiki/Isidor_Isaac_Rabi" title="Isidor Isaac Rabi">Rabi</a></li> <li><a href="/wiki/C._V._Raman" title="C. V. Raman">Raman</a></li> <li><a href="/wiki/Johannes_Rydberg" title="Johannes Rydberg">Rydberg</a></li> <li><a href="/wiki/Erwin_Schr%C3%B6dinger" title="Erwin Schrödinger">Schrödinger</a></li> <li><a href="/wiki/Michelle_Simmons" title="Michelle Simmons">Simmons</a></li> <li><a href="/wiki/Arnold_Sommerfeld" title="Arnold Sommerfeld">Sommerfeld</a></li> <li><a href="/wiki/John_von_Neumann" title="John von Neumann">von Neumann</a></li> <li><a href="/wiki/Hermann_Weyl" title="Hermann Weyl">Weyl</a></li> <li><a href="/wiki/Wilhelm_Wien" title="Wilhelm Wien">Wien</a></li> <li><a href="/wiki/Eugene_Wigner" title="Eugene Wigner">Wigner</a></li> <li><a href="/wiki/Pieter_Zeeman" title="Pieter Zeeman">Zeeman</a></li> <li><a href="/wiki/Anton_Zeilinger" title="Anton Zeilinger">Zeilinger</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-navbar" style="border-top:1px solid #aaa;padding-top:0.1em;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a 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" title="Template:Quantum mechanics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Quantum_mechanics" title="Template talk:Quantum mechanics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Quantum_mechanics" title="Special:EditPage/Template:Quantum mechanics"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>Quantum mechanics</b> is the study of <a href="/wiki/Matter" title="Matter">matter</a> and its interactions with <a href="/wiki/Energy" title="Energy">energy</a> on the <a href="/wiki/Orders_of_magnitude_(length)" title="Orders of magnitude (length)">scale</a> of <a href="/wiki/Atom" title="Atom">atomic</a> and <a href="/wiki/Elementary_particle" title="Elementary particle">subatomic particles</a>. By contrast, <a href="/wiki/Classical_physics" title="Classical physics">classical physics</a> explains matter and energy only on a scale familiar to human experience, including the behavior of astronomical bodies such as the moon. Classical physics is still used in much of modern science and technology. However, towards the end of the 19th century, scientists discovered phenomena in both the large (<a href="/wiki/Macroscopic_scale" title="Macroscopic scale">macro</a>) and the small (<a href="/wiki/Microscopic_scale" title="Microscopic scale">micro</a>) worlds that classical physics could not explain.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> The desire to resolve inconsistencies between observed phenomena and classical theory led to a revolution in physics, a shift in the original <a href="/wiki/Scientific_paradigm" class="mw-redirect" title="Scientific paradigm">scientific paradigm</a>:<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> the development of <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a>. </p><p>Many aspects of quantum mechanics are counterintuitive<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> and can seem <a href="/wiki/Paradox" title="Paradox">paradoxical</a> because they describe behavior quite different from that seen at larger scales. In the words of quantum physicist <a href="/wiki/Richard_Feynman" title="Richard Feynman">Richard Feynman</a>, quantum mechanics deals with "nature as She is—absurd".<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> Features of quantum mechanics often defy simple explanations in everyday language. One example of this is the <a href="/wiki/Uncertainty_principle" title="Uncertainty principle">uncertainty principle</a>: precise measurements of position cannot be combined with precise measurements of velocity. Another example is <a href="/wiki/Quantum_entanglement" title="Quantum entanglement">entanglement</a>: a measurement made on one particle (such as an <a href="/wiki/Electron" title="Electron">electron</a> that is measured to have <a href="/wiki/Spin_(physics)" title="Spin (physics)">spin</a> 'up') will correlate with a measurement on a second particle (an electron will be found to have spin 'down') if the two particles have a shared history. This will apply even if it is impossible for the result of the first measurement to have been transmitted to the second particle before the second measurement takes place. </p><p>Quantum mechanics helps us understand <a href="/wiki/Chemistry" title="Chemistry">chemistry</a>, because it explains how atoms interact with each other and form <a href="/wiki/Molecule" title="Molecule">molecules</a>. Many remarkable phenomena can be explained using quantum mechanics, like <a href="/wiki/Superfluidity" title="Superfluidity">superfluidity</a>. For example, if liquid <a href="/wiki/Helium" title="Helium">helium</a> cooled to a temperature near <a href="/wiki/Absolute_zero" title="Absolute zero">absolute zero</a> is placed in a container, it spontaneously flows up and over the rim of its container; this is an effect which cannot be explained by classical physics. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Introduction_to_quantum_mechanics&action=edit&section=1" title="Edit section: History"><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/History_of_quantum_mechanics" title="History of quantum mechanics">History of quantum mechanics</a></div> <p><a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">James C. Maxwell</a>'s <a href="/wiki/History_of_Maxwell%27s_equations" title="History of Maxwell's equations">unification of the equations</a> governing electricity, magnetism, and light in the late 19th century led to experiments on the interaction of light and matter. Some of these experiments had aspects which could not be explained until quantum mechanics emerged in the early part of the 20th century.<sup id="cite_ref-Whittaker_5-0" class="reference"><a href="#cite_note-Whittaker-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Evidence_of_quanta_from_the_photoelectric_effect">Evidence of quanta from the photoelectric effect</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Introduction_to_quantum_mechanics&action=edit&section=2" title="Edit section: Evidence of quanta from 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> <p>The seeds of the quantum revolution appear in the discovery by <a href="/wiki/J.J._Thomson" class="mw-redirect" title="J.J. Thomson">J.J. Thomson</a> in 1897 that <a href="/wiki/Cathode_rays" class="mw-redirect" title="Cathode rays">cathode rays</a> were not continuous but "corpuscles" (<a href="/wiki/Electrons" class="mw-redirect" title="Electrons">electrons</a>). Electrons had been named just six years earlier as part of the emerging theory of <a href="/wiki/Atoms" class="mw-redirect" title="Atoms">atoms</a>. In 1900, <a href="/wiki/Max_Planck" title="Max Planck">Max Planck</a>, unconvinced by the <a href="/wiki/Atomic_theory" class="mw-redirect" title="Atomic theory">atomic theory</a>, discovered that he needed discrete entities like atoms or electrons to explain <a href="/wiki/Black-body_radiation" title="Black-body radiation">black-body radiation</a>.<sup id="cite_ref-Baggott_6-0" class="reference"><a href="#cite_note-Baggott-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </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><a href="/wiki/Black-body_radiation" title="Black-body radiation">Black-body radiation</a> intensity vs color and temperature. The rainbow bar represents visible light; 5000 <a href="/wiki/Kelvin" title="Kelvin">K</a> objects are "white hot" by mixing differing colors of visible light. To the right is the invisible infrared. Classical theory (black curve for 5000 K) fails to predict the colors; the other curves are correctly predicted by quantum theories.</figcaption></figure> <p>Very hot – red hot or white hot – objects look similar when heated to the same temperature. This look results from a common curve of light intensity at different frequencies (colors), which is called black-body radiation. White hot objects have intensity across many colors in the visible range. The lowest frequencies above visible colors are <a href="/wiki/Infrared_light" class="mw-redirect" title="Infrared light">infrared light</a>, which also give off heat. Continuous wave theories of light and matter cannot explain the black-body radiation curve. Planck spread the heat energy among individual "oscillators" of an undefined character but with discrete energy capacity; this model explained black-body radiation. </p><p>At the time, electrons, atoms, and discrete oscillators were all exotic ideas to explain exotic phenomena. But in 1905 <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> proposed that light was also corpuscular, consisting of "energy quanta", in contradiction to the established science of light as a continuous wave, stretching back a hundred years to <a href="/wiki/Thomas_Young_(scientist)" title="Thomas Young (scientist)">Thomas Young</a>'s work on <a href="/wiki/Diffraction" title="Diffraction">diffraction</a>. </p><p>Einstein's revolutionary proposal started by reanalyzing Planck's black-body theory, arriving at the same conclusions by using the new "energy quanta". Einstein then showed how energy quanta connected to Thomson's electron. In 1902, <a href="/wiki/Philipp_Lenard" title="Philipp Lenard">Philipp Lenard</a> directed light from an arc lamp onto freshly cleaned metal plates housed in an evacuated glass tube. He measured the electric current coming off the metal plate, at higher and lower intensities of light and for different metals. Lenard showed that amount of current – the number of electrons – depended on the intensity of the light, but that the velocity of these electrons did not depend on intensity. This is the <a href="/wiki/Photoelectric_effect" title="Photoelectric effect">photoelectric effect</a>. The continuous wave theories of the time predicted that more light intensity would accelerate the same amount of current to higher velocity, contrary to this experiment. Einstein's energy quanta explained the volume increase: one electron is ejected for each quantum: more quanta mean more electrons.<sup id="cite_ref-Baggott_6-1" class="reference"><a href="#cite_note-Baggott-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 23">: 23 </span></sup> </p><p>Einstein then predicted that the electron velocity would increase in direct proportion to the light frequency above a fixed value that depended upon the metal. Here the idea is that energy in energy-quanta depends upon the light frequency; the energy transferred to the electron comes in proportion to the light frequency. The type of metal gives a <a href="/wiki/Work_function" title="Work function">barrier</a>, the fixed value, that the electrons must climb over to exit their atoms, to be emitted from the metal surface and be measured. </p><p>Ten years elapsed before Millikan's definitive experiment<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> verified Einstein's prediction. During that time many scientists rejected the revolutionary idea of quanta.<sup id="cite_ref-pais_8-0" class="reference"><a href="#cite_note-pais-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> But Planck's and Einstein's concept was in the air and soon began to affect other physics and quantum theories. </p> <div class="mw-heading mw-heading3"><h3 id="Quantization_of_bound_electrons_in_atoms">Quantization of bound electrons in atoms</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Introduction_to_quantum_mechanics&action=edit&section=3" title="Edit section: Quantization of bound electrons in atoms"><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 articles: <a href="/wiki/Atomic_theory" class="mw-redirect" title="Atomic theory">Atomic theory</a>, <a href="/wiki/Bohr_atom" class="mw-redirect" title="Bohr atom">Bohr atom</a>, and <a href="/wiki/Bohr-Sommerfeld_model" class="mw-redirect" title="Bohr-Sommerfeld model">Bohr-Sommerfeld model</a></div> <p>Experiments with light and matter in the late 1800s uncovered a reproducible but puzzling regularity. When light was shown through purified gases, certain frequencies (colors) did not pass. These dark absorption 'lines' followed a distinctive pattern: the gaps between the lines decreased steadily. By 1889, the <a href="/wiki/Rydberg_formula" title="Rydberg formula">Rydberg formula</a> predicted the lines for hydrogen gas using only a constant number and the integers to index the lines.<sup id="cite_ref-Whittaker_5-1" class="reference"><a href="#cite_note-Whittaker-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: v1:376">: v1:376 </span></sup> The origin of this regularity was unknown. Solving this mystery would eventually become the first major step toward quantum mechanics. </p><p>Throughout the 19th century evidence grew for the <a href="/wiki/Atomic_theory" class="mw-redirect" title="Atomic theory">atomic</a> nature of matter. With Thomson's discovery of the electron in 1897, scientist began the search for a model of the interior of the atom. Thomson proposed <a href="/wiki/Plum_pudding_model" title="Plum pudding model">negative electrons swimming in a pool of positive charge</a>. Between 1908 and 1911, <a href="/wiki/Rutherford_model" title="Rutherford model">Rutherford</a> showed that the positive part was only 1/3000th of the diameter of the atom.<sup id="cite_ref-Baggott_6-2" class="reference"><a href="#cite_note-Baggott-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 26">: 26 </span></sup> </p><p>Models of "planetary" electrons orbiting a nuclear "Sun" were proposed, but cannot explain why the electron does not simply fall into the positive charge. In 1913 Niels Bohr and Ernest Rutherford connected the new atom models to the mystery of the Rydberg formula: the orbital radius of the electrons were constrained and the resulting energy differences matched the energy differences in the absorption lines. This meant that absorption and emission of light from atoms was energy quantized: only specific energies that matched the difference in orbital energy would be emitted or absorbed.<sup id="cite_ref-Baggott_6-3" class="reference"><a href="#cite_note-Baggott-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 31">: 31 </span></sup> </p><p>Trading one mystery – the regular pattern of the Rydberg formula – for another mystery – constraints on electron orbits – might not seem like a big advance, but the new atom model summarized many other experimental findings. The quantization of the photoelectric effect and now the quantization of the electron orbits set the stage for the final revolution. </p><p>Throughout the first and the modern era of quantum mechanics the concept that classical mechanics must be valid macroscopically constrained possible quantum models. This concept was formalized by Bohr in 1923 as the <a href="/wiki/Correspondence_principle" title="Correspondence principle">correspondence principle</a>. It requires quantum theory to converge to classical limits.<sup id="cite_ref-messiah_9-0" class="reference"><a href="#cite_note-messiah-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 29">: 29 </span></sup> A related concept is <a href="/wiki/Ehrenfest%27s_theorem" class="mw-redirect" title="Ehrenfest's theorem">Ehrenfest's theorem</a>, which shows that the average values obtained from quantum mechanics (e.g. position and momentum) obey classical laws.<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> </p> <div class="mw-heading mw-heading3"><h3 id="Quantization_of_spin">Quantization of spin</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Introduction_to_quantum_mechanics&action=edit&section=4" title="Edit section: Quantization of spin"><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/Stern%E2%80%93Gerlach_experiment" title="Stern–Gerlach experiment">Stern–Gerlach experiment</a></div><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Stern-Gerlach_experiment_svg.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Stern-Gerlach_experiment_svg.svg/300px-Stern-Gerlach_experiment_svg.svg.png" decoding="async" width="300" height="212" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Stern-Gerlach_experiment_svg.svg/450px-Stern-Gerlach_experiment_svg.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Stern-Gerlach_experiment_svg.svg/600px-Stern-Gerlach_experiment_svg.svg.png 2x" data-file-width="1052" data-file-height="744" /></a><figcaption><b>Stern–Gerlach experiment</b>: Silver atoms travelling through an inhomogeneous magnetic field, and being deflected up or down depending on their spin; (1) furnace, (2) beam of silver atoms, (3) inhomogeneous magnetic field, (4) classically expected result, (5) observed result</figcaption></figure> <p>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> <a href="/wiki/Stern%E2%80%93Gerlach_experiment" title="Stern–Gerlach experiment">demonstrated</a> that the magnetic properties of silver atoms defy classical explanation, the work contributing to Stern’s 1943 <a href="/wiki/Nobel_Prize_in_Physics" title="Nobel Prize in Physics">Nobel Prize in Physics</a>. They fired a beam of silver atoms through a magnetic field. According to classical physics, the atoms should have emerged in a spray, with a continuous range of directions. Instead, the beam separated into two, and only two, diverging streams of atoms.<sup id="cite_ref-cigar_11-0" class="reference"><a href="#cite_note-cigar-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Unlike the other quantum effects known at the time, this striking result involves the state of a single atom.<sup id="cite_ref-Whittaker_5-2" class="reference"><a href="#cite_note-Whittaker-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: v2:130">: v2:130 </span></sup> In 1927, T.E. Phipps and J.B. Taylor obtained a similar, but less pronounced effect using <a href="/wiki/Hydrogen" title="Hydrogen">hydrogen</a> atoms in their <a href="/wiki/Ground_state" title="Ground state">ground state</a>, thereby eliminating any doubts that may have been caused by the use of <a href="/wiki/Silver" title="Silver">silver</a> atoms.<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> </p><p>In 1924, Wolfgang Pauli called it "two-valuedness not describable classically" and associated it with electrons in the outermost shell.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> The experiments lead to formulation of its theory described to arise from spin of the electron in 1925, by <a href="/wiki/Samuel_Goudsmit" title="Samuel Goudsmit">Samuel Goudsmit</a> and <a href="/wiki/George_Uhlenbeck" title="George Uhlenbeck">George Uhlenbeck</a>, under the advice of <a href="/wiki/Paul_Ehrenfest" title="Paul Ehrenfest">Paul Ehrenfest</a>.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Quantization_of_matter">Quantization of matter</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Introduction_to_quantum_mechanics&action=edit&section=5" title="Edit section: Quantization of matter"><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 articles: <a href="/wiki/Matter_wave" title="Matter wave">Matter wave</a> and <a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger equation</a></div><p>In 1924 <a href="/wiki/Louis_de_Broglie" title="Louis de Broglie">Louis de Broglie</a> proposed<sup id="cite_ref-Broglie_15-0" class="reference"><a href="#cite_note-Broglie-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> that electrons in an atom are constrained not in "orbits" but as standing waves. In detail his solution did not work, but his hypothesis – that the electron "corpuscle" moves in the atom as a wave – spurred <a href="/wiki/Erwin_Schr%C3%B6dinger" title="Erwin Schrödinger">Erwin Schrödinger</a> to develop a <a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">wave equation</a> for electrons; when applied to hydrogen the Rydberg formula was accurately reproduced.<sup id="cite_ref-Baggott_6-4" class="reference"><a href="#cite_note-Baggott-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 65">: 65 </span></sup> </p><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:A565_G_P_Thomson_Electron_Diffraction.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/A565_G_P_Thomson_Electron_Diffraction.jpg/220px-A565_G_P_Thomson_Electron_Diffraction.jpg" decoding="async" width="220" height="222" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/A565_G_P_Thomson_Electron_Diffraction.jpg/330px-A565_G_P_Thomson_Electron_Diffraction.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7f/A565_G_P_Thomson_Electron_Diffraction.jpg/440px-A565_G_P_Thomson_Electron_Diffraction.jpg 2x" data-file-width="1525" data-file-height="1536" /></a><figcaption>Example original electron diffraction photograph from the laboratory of G. P. Thomson, recorded 1925–1927</figcaption></figure> <p><a href="/wiki/Max_Born" title="Max Born">Max Born</a>'s 1924 paper <i>"Zur Quantenmechanik"</i> was the first use of the words "quantum mechanics" in print.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> His later work included developing quantum collision models; in a footnote to a 1926 paper he proposed the <a href="/wiki/Born_rule" title="Born rule">Born rule</a> connecting theoretical models to experiment.<sup id="cite_ref-Zeitschrift_18-0" class="reference"><a href="#cite_note-Zeitschrift-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p><p>In 1927 at Bell Labs, <a href="/wiki/Clinton_Davisson" title="Clinton Davisson">Clinton Davisson</a> and <a href="/wiki/Lester_Germer" title="Lester Germer">Lester Germer</a> <a href="/wiki/Davisson%E2%80%93Germer_experiment" title="Davisson–Germer experiment">fired</a> slow-moving <a href="/wiki/Electron" title="Electron">electrons</a> at a <a href="/wiki/Crystal" title="Crystal">crystalline</a> <a href="/wiki/Nickel" title="Nickel">nickel</a> target which showed a diffraction pattern<sup id="cite_ref-DG12_19-0" class="reference"><a href="#cite_note-DG12-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-DG22_20-0" class="reference"><a href="#cite_note-DG22-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-DG02_21-0" class="reference"><a href="#cite_note-DG02-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:02_22-0" class="reference"><a href="#cite_note-:02-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> indicating wave nature of electron whose theory was fully explained by <a href="/wiki/Hans_Bethe" title="Hans Bethe">Hans Bethe</a>.<sup id="cite_ref-Bethe_23-0" class="reference"><a href="#cite_note-Bethe-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> A similar experiment by <a href="/wiki/George_Paget_Thomson" title="George Paget Thomson">George Paget Thomson</a> and Alexander Reid, firing electrons at thin celluloid foils and later metal films, observing rings, independently discovered matter wave nature of electrons.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Further_developments">Further developments</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Introduction_to_quantum_mechanics&action=edit&section=6" title="Edit section: Further developments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1928 <a href="/wiki/Paul_Dirac" title="Paul Dirac">Paul Dirac</a> published his <a href="/wiki/Dirac_equation" title="Dirac equation">relativistic wave equation</a> simultaneously incorporating <a href="/wiki/Theory_of_relativity" title="Theory of relativity">relativity</a>, predicting <a href="/wiki/Anti-matter" class="mw-redirect" title="Anti-matter">anti-matter</a>, and providing a complete theory for the Stern–Gerlach result.<sup id="cite_ref-Baggott_6-5" class="reference"><a href="#cite_note-Baggott-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 131">: 131 </span></sup> These successes launched a new fundamental understanding of our world at small scale: <a href="/wiki/Quantum_mechanics" title="Quantum mechanics"><i><b>quantum mechanics.</b></i></a> </p><p>Planck and Einstein started the revolution with quanta that broke down the continuous models of matter and light. Twenty years later "corpuscles" like electrons came to be modeled as continuous waves. This result came to be called wave-particle duality, one iconic idea along with the uncertainty principle that sets quantum mechanics apart from older models of physics. </p> <div class="mw-heading mw-heading3"><h3 id="Quantum_radiation,_quantum_fields"><span id="Quantum_radiation.2C_quantum_fields"></span>Quantum radiation, quantum fields</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Introduction_to_quantum_mechanics&action=edit&section=7" title="Edit section: Quantum radiation, quantum fields"><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/History_of_quantum_field_theory" title="History of quantum field theory">History of quantum field theory</a></div> <p>In 1923 <a href="/wiki/Compton_scattering" title="Compton scattering">Compton</a> demonstrated that the Planck-Einstein energy quanta from light also had momentum; three years later the "energy quanta" got a new name "<a href="/wiki/Photon" title="Photon">photon</a>"<sup id="cite_ref-photon-named_25-0" class="reference"><a href="#cite_note-photon-named-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> Despite its role in almost all stages of the quantum revolution, no explicit model for light quanta existed until 1927 when <a href="/wiki/Paul_Dirac" title="Paul Dirac">Paul Dirac</a> began work on a quantum theory of radiation<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> that became <a href="/wiki/Quantum_electrodynamics" title="Quantum electrodynamics">quantum electrodynamics</a>. Over the following decades this work evolved into <a href="/wiki/Quantum_field_theory" title="Quantum field theory">quantum field theory</a>, the basis for modern <a href="/wiki/Quantum_optics" title="Quantum optics">quantum optics</a> and <a href="/wiki/Particle_physics" title="Particle physics">particle physics</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Wave–particle_duality"><span id="Wave.E2.80.93particle_duality"></span>Wave–particle duality</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Introduction_to_quantum_mechanics&action=edit&section=8" title="Edit section: Wave–particle duality"><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 articles: <a href="/wiki/Wave%E2%80%93particle_duality" title="Wave–particle duality">Wave–particle duality</a> and <a href="/wiki/Double-slit_experiment" title="Double-slit experiment">Double-slit experiment</a></div> <p>The concept of wave–particle duality says that neither the classical concept of "particle" nor of "wave" can fully describe the behavior of quantum-scale objects, either photons or matter. Wave–particle duality is an example of the <a href="/wiki/Complementarity_(physics)" title="Complementarity (physics)">principle of complementarity</a> in quantum physics.<sup id="cite_ref-Zettili_27-0" class="reference"><a href="#cite_note-Zettili-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Selleri_28-0" class="reference"><a href="#cite_note-Selleri-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Podgorsak_29-0" class="reference"><a href="#cite_note-Podgorsak-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Halliday&Resnick_30-0" class="reference"><a href="#cite_note-Halliday&Resnick-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Myers_31-0" class="reference"><a href="#cite_note-Myers-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> An elegant example of wave-particle duality is the double-slit experiment. </p> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Single_slit_and_double_slit2.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Single_slit_and_double_slit2.jpg/330px-Single_slit_and_double_slit2.jpg" decoding="async" width="330" height="249" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Single_slit_and_double_slit2.jpg/495px-Single_slit_and_double_slit2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/c/c2/Single_slit_and_double_slit2.jpg 2x" data-file-width="560" data-file-height="422" /></a><figcaption>The diffraction pattern produced when light is shone through one slit (top) and the interference pattern produced by two slits (bottom). Both patterns show oscillations due to the wave nature of light. The double slit pattern is more dramatic.</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><span><video id="mwe_player_0" poster="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Wave-particle_duality.ogv/220px--Wave-particle_duality.ogv.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" height="124" data-durationhint="117" data-mwtitle="Wave-particle_duality.ogv" data-mwprovider="wikimediacommons" resource="/wiki/File:Wave-particle_duality.ogv"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e4/Wave-particle_duality.ogv/Wave-particle_duality.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/e/e4/Wave-particle_duality.ogv/Wave-particle_duality.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/e/e4/Wave-particle_duality.ogv" type="video/ogg; codecs="theora, vorbis"" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e4/Wave-particle_duality.ogv/Wave-particle_duality.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/e/e4/Wave-particle_duality.ogv/Wave-particle_duality.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/e/e4/Wave-particle_duality.ogv/Wave-particle_duality.ogv.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /></video></span><figcaption>The double-slit experiment for a classical particle, a wave, and a quantum particle demonstrating wave-particle duality</figcaption></figure> <p>In the double-slit experiment, as originally performed by <a href="/wiki/Thomas_Young_(scientist)" title="Thomas Young (scientist)">Thomas Young</a> in 1803,<sup id="cite_ref-ShamosGreatExperiments_32-0" class="reference"><a href="#cite_note-ShamosGreatExperiments-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> and then <a href="/wiki/Augustin_Fresnel" class="mw-redirect" title="Augustin Fresnel">Augustin Fresnel</a> a decade later,<sup id="cite_ref-ShamosGreatExperiments_32-1" class="reference"><a href="#cite_note-ShamosGreatExperiments-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> a beam of light is directed through two narrow, closely spaced slits, producing an <a href="/wiki/Interference_(wave_propagation)" class="mw-redirect" title="Interference (wave propagation)">interference pattern</a> of light and dark bands on a screen. The same behavior can be demonstrated in water waves: the double-slit experiment was seen as a demonstration of the wave nature of light. </p><p>Variations of the double-slit experiment have been performed using electrons, atoms, and even large molecules,<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> and the same type of interference pattern is seen. Thus it has been demonstrated that all <a href="/wiki/Matter" title="Matter">matter</a> possesses wave characteristics. </p><p>If the source intensity is turned down, the same interference pattern will slowly build up, one "count" or particle (e.g. photon or electron) at a time. The quantum system acts as a wave when passing through the double slits, but as a particle when it is detected. This is a typical feature of quantum complementarity: a quantum system acts as a wave in an experiment to measure its wave-like properties, and like a particle in an experiment to measure its particle-like properties. The point on the detector screen where any individual particle shows up is the result of a random process. However, the distribution pattern of many individual particles mimics the diffraction pattern produced by waves. </p> <div class="mw-heading mw-heading2"><h2 id="Uncertainty_principle">Uncertainty principle</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Introduction_to_quantum_mechanics&action=edit&section=9" title="Edit section: Uncertainty principle"><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/Uncertainty_principle" title="Uncertainty principle">Uncertainty principle</a></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Heisenberg_10.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Heisenberg_10.jpg/170px-Heisenberg_10.jpg" decoding="async" width="170" height="251" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Heisenberg_10.jpg/255px-Heisenberg_10.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Heisenberg_10.jpg/340px-Heisenberg_10.jpg 2x" data-file-width="542" data-file-height="800" /></a><figcaption><a href="/wiki/Werner_Heisenberg" title="Werner Heisenberg">Werner Heisenberg</a> at the age of 26. Heisenberg won the <a href="/wiki/Nobel_Prize_in_Physics" title="Nobel Prize in Physics">Nobel Prize in Physics</a> in 1932 for the work he did in the late 1920s.<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>Suppose it is desired to measure the position and speed of an object—for example, a car going through a radar speed trap. It can be assumed that the car has a definite position and speed at a particular moment in time. How accurately these values can be measured depends on the quality of the measuring equipment. If the precision of the measuring equipment is improved, it provides a result closer to the true value. It might be assumed that the speed of the car and its position could be operationally defined and measured simultaneously, as precisely as might be desired. </p><p>In 1927, Heisenberg proved that this last assumption is not correct.<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> Quantum mechanics shows that certain pairs of physical properties, for example, position and speed, cannot be simultaneously measured, nor defined in operational terms, to arbitrary precision: the more precisely one property is measured, or defined in operational terms, the less precisely can the other be thus treated. This statement is known as the <a href="/wiki/Uncertainty_principle" title="Uncertainty principle">uncertainty principle</a>. The uncertainty principle is not only a statement about the accuracy of our measuring equipment but, more deeply, is about the conceptual nature of the measured quantities—the assumption that the car had simultaneously defined position and speed does not work in quantum mechanics. On a scale of cars and people, these uncertainties are negligible, but when dealing with atoms and electrons they become critical.<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> </p><p>Heisenberg gave, as an illustration, the measurement of the position and <a href="/wiki/Momentum" title="Momentum">momentum</a> of an electron using a photon of light. In measuring the electron's position, the higher the frequency of the photon, the more accurate is the measurement of the position of the impact of the photon with the electron, but the greater is the disturbance of the electron. This is because from the impact with the photon, the electron absorbs a random amount of energy, rendering the measurement obtained of its momentum increasingly uncertain, for one is necessarily measuring its post-impact disturbed momentum from the collision products and not its original momentum (momentum which should be simultaneously measured with position). With a photon of lower frequency, the disturbance (and hence uncertainty) in the momentum is less, but so is the accuracy of the measurement of the position of the impact.<sup id="cite_ref-EB-uncertainty_38-0" class="reference"><a href="#cite_note-EB-uncertainty-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> </p><p>At the heart of the uncertainty principle is a fact that for any mathematical analysis in the position and velocity domains, achieving a sharper (more precise) curve in the position domain can only be done at the expense of a more gradual (less precise) curve in the speed domain, and vice versa. More sharpness in the position domain requires contributions from more frequencies in the speed domain to create the narrower curve, and vice versa. It is a fundamental tradeoff inherent in any such related or <a href="/wiki/Complementarity_(physics)" title="Complementarity (physics)">complementary</a> measurements, but is only really noticeable at the smallest (Planck) scale, near the size of <a href="/wiki/Elementary_particles" class="mw-redirect" title="Elementary particles">elementary particles</a>. </p><p>The uncertainty principle shows mathematically that the product of the uncertainty in the position and <a href="/wiki/Momentum" title="Momentum">momentum</a> of a particle (momentum is velocity multiplied by mass) could never be less than a certain value, and that this value is related to the <a href="/wiki/Planck_constant" title="Planck constant">Planck constant</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Wave_function_collapse">Wave function collapse</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Introduction_to_quantum_mechanics&action=edit&section=10" title="Edit section: Wave function collapse"><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/Wave_function_collapse" title="Wave function collapse">Wave function collapse</a></div> <p><i>Wave function collapse</i> means that a measurement has forced or converted a quantum (probabilistic or potential) state into a definite measured value. This phenomenon is only seen in quantum mechanics rather than classical mechanics. </p><p>For example, before a photon actually "shows up" on a detection screen it can be described only with a set of probabilities for where it might show up. When it does appear, for instance in the <a href="/wiki/Charge-coupled_device" title="Charge-coupled device">CCD</a> of an electronic camera, the time and space where it interacted with the device are known within very tight limits. However, the photon has disappeared in the process of being captured (measured), and its quantum <a href="/wiki/Wave_function" title="Wave function">wave function</a> has disappeared with it. In its place, some macroscopic physical change in the detection screen has appeared, e.g., an exposed spot in a sheet of photographic film, or a change in electric potential in some cell of a CCD. </p> <div class="mw-heading mw-heading2"><h2 id="Eigenstates_and_eigenvalues">Eigenstates and eigenvalues</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Introduction_to_quantum_mechanics&action=edit&section=11" title="Edit section: Eigenstates and eigenvalues"><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">Further information: <a href="/wiki/Introduction_to_eigenstates" class="mw-redirect" title="Introduction to eigenstates">Introduction to eigenstates</a></div> <p>Because of the uncertainty principle, statements about both the position and momentum of particles can assign only a <a href="/wiki/Probability" title="Probability">probability</a> that the position or momentum has some numerical value. Therefore, it is necessary to formulate clearly the difference between the state of something indeterminate, such as an electron in a probability cloud, and the state of something having a definite value. When an object can definitely be "pinned-down" in some respect, it is said to possess an <a href="/wiki/Eigenstate" class="mw-redirect" title="Eigenstate">eigenstate</a>. </p><p>In the Stern–Gerlach experiment discussed <a href="#Spin">above</a>, the quantum model predicts two possible values of spin for the atom compared to the magnetic axis. These two eigenstates are named arbitrarily 'up' and 'down'. The quantum model predicts these states will be measured with equal probability, but no intermediate values will be seen. This is what the Stern–Gerlach experiment shows. </p><p>The eigenstates of spin about the vertical axis are not simultaneously eigenstates of spin about the horizontal axis, so this atom has an equal probability of being found to have either value of spin about the horizontal axis. As described in the section <a href="#Spin">above</a>, measuring the spin about the horizontal axis can allow an atom that was spun up to spin down: measuring its spin about the horizontal axis collapses its wave function into one of the eigenstates of this measurement, which means it is no longer in an eigenstate of spin about the vertical axis, so can take either value. </p> <div class="mw-heading mw-heading2"><h2 id="The_Pauli_exclusion_principle">The Pauli exclusion principle</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Introduction_to_quantum_mechanics&action=edit&section=12" title="Edit section: The Pauli exclusion principle"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Wolfgang_Pauli_young.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/43/Wolfgang_Pauli_young.jpg/170px-Wolfgang_Pauli_young.jpg" decoding="async" width="170" height="204" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/4/43/Wolfgang_Pauli_young.jpg 1.5x" data-file-width="250" data-file-height="300" /></a><figcaption><a href="/wiki/Wolfgang_Pauli" title="Wolfgang Pauli">Wolfgang Pauli</a></figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Pauli_exclusion_principle" title="Pauli exclusion principle">Pauli exclusion principle</a></div> <p>In 1924, <a href="/wiki/Wolfgang_Pauli" title="Wolfgang Pauli">Wolfgang Pauli</a> proposed a new quantum degree of freedom (or <a href="/wiki/Quantum_number" title="Quantum number">quantum number</a>), with two possible values, to resolve inconsistencies between observed molecular spectra and the predictions of quantum mechanics. In particular, the <a href="/wiki/Hydrogen_spectrum" class="mw-redirect" title="Hydrogen spectrum">spectrum of atomic hydrogen</a> had a <a href="/wiki/Doublet_(physics)" class="mw-redirect" title="Doublet (physics)">doublet</a>, or pair of lines differing by a small amount, where only one line was expected. Pauli formulated his <i>exclusion principle</i>, stating, "There cannot exist an atom in such a quantum state that two electrons within [it] have the same set of quantum numbers."<sup id="cite_ref-Pauling_39-0" class="reference"><a href="#cite_note-Pauling-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> </p><p>A year later, <a href="/wiki/George_Eugene_Uhlenbeck" class="mw-redirect" title="George Eugene Uhlenbeck">Uhlenbeck</a> and <a href="/wiki/Samuel_Goudsmit" title="Samuel Goudsmit">Goudsmit</a> identified Pauli's new degree of freedom with the property called <a href="/wiki/Spin_(physics)" title="Spin (physics)">spin</a> whose effects were observed in the <a href="/wiki/Stern%E2%80%93Gerlach_experiment" title="Stern–Gerlach experiment">Stern–Gerlach experiment</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Dirac_wave_equation">Dirac wave equation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Introduction_to_quantum_mechanics&action=edit&section=13" title="Edit section: Dirac wave equation"><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/Dirac_equation" title="Dirac equation">Dirac equation</a></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Paul_Dirac,_1933,_head_and_shoulders_portrait,_bw.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Paul_Dirac%2C_1933%2C_head_and_shoulders_portrait%2C_bw.jpg/170px-Paul_Dirac%2C_1933%2C_head_and_shoulders_portrait%2C_bw.jpg" decoding="async" width="170" height="212" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Paul_Dirac%2C_1933%2C_head_and_shoulders_portrait%2C_bw.jpg/255px-Paul_Dirac%2C_1933%2C_head_and_shoulders_portrait%2C_bw.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/8/8a/Paul_Dirac%2C_1933%2C_head_and_shoulders_portrait%2C_bw.jpg 2x" data-file-width="261" data-file-height="326" /></a><figcaption>Paul Dirac (1902–1984)</figcaption></figure> <p>In 1928, Paul Dirac extended the <a href="/wiki/Pauli_equation" title="Pauli equation">Pauli equation</a>, which described spinning electrons, to account for <a href="/wiki/Special_relativity" title="Special relativity">special relativity</a>. The result was a theory that dealt properly with events, such as the speed at which an electron orbits the nucleus, occurring at a substantial fraction of the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a>. By using the simplest <a href="/wiki/Electromagnetic_interaction" class="mw-redirect" title="Electromagnetic interaction">electromagnetic interaction</a>, Dirac was able to predict the value of the magnetic moment associated with the electron's spin and found the experimentally observed value, which was too large to be that of a spinning charged sphere governed by <a href="/wiki/Classical_physics" title="Classical physics">classical physics</a>. He was able to solve for the <a href="/wiki/Hydrogen_spectrum" class="mw-redirect" title="Hydrogen spectrum">spectral lines of the hydrogen atom</a> and to reproduce from physical first principles <a href="/wiki/Arnold_Sommerfeld" title="Arnold Sommerfeld">Sommerfeld</a>'s successful formula for the <a href="/wiki/Fine_structure" title="Fine structure">fine structure</a> of the hydrogen spectrum. </p><p>Dirac's equations sometimes yielded a negative value for energy, for which he proposed a novel solution: he posited the existence of an <a href="/wiki/Antielectron" class="mw-redirect" title="Antielectron">antielectron</a> and a dynamical vacuum. This led to the many-particle <a href="/wiki/Quantum_field_theory" title="Quantum field theory">quantum field theory</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Quantum_entanglement">Quantum entanglement</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Introduction_to_quantum_mechanics&action=edit&section=14" title="Edit section: Quantum entanglement"><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/Quantum_entanglement" title="Quantum entanglement">Quantum entanglement</a></div> <p>In quantum physics, a group of <a href="/wiki/Particle" title="Particle">particles</a> can interact or be created together in such a way that the <a href="/wiki/Quantum_state" title="Quantum state">quantum state</a> of each particle of the group cannot be described independently of the state of the others, including when the particles are separated by a large distance. This is known as <a href="/wiki/Quantum_entanglement" title="Quantum entanglement">quantum entanglement</a>. </p><p>An early landmark in the study of entanglement was the <a href="/wiki/EPR_paradox" class="mw-redirect" title="EPR paradox">Einstein–Podolsky–Rosen (EPR) paradox</a>, a <a href="/wiki/Thought_experiment" title="Thought experiment">thought experiment</a> proposed by Albert Einstein, <a href="/wiki/Boris_Podolsky" title="Boris Podolsky">Boris Podolsky</a> and <a href="/wiki/Nathan_Rosen" title="Nathan Rosen">Nathan Rosen</a> which argues that the description of physical reality provided by <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a> is incomplete.<sup id="cite_ref-EPR_40-0" class="reference"><a href="#cite_note-EPR-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> In a 1935 paper titled "Can Quantum-Mechanical Description of Physical Reality be Considered Complete?", they argued for the existence of "elements of reality" that were not part of quantum theory, and speculated that it should be possible to construct a theory containing these <a href="/wiki/Hidden-variable_theory" title="Hidden-variable theory">hidden variables</a>. </p><p>The thought experiment involves a pair of particles prepared in what would later become known as an entangled state. Einstein, Podolsky, and Rosen pointed out that, in this state, if the position of the first particle were measured, the result of measuring the position of the second particle could be predicted. If instead the momentum of the first particle were measured, then the result of measuring the momentum of the second particle could be predicted. They argued that no action taken on the first particle could instantaneously affect the other, since this would involve information being transmitted faster than light, which is forbidden by the <a href="/wiki/Theory_of_relativity" title="Theory of relativity">theory of relativity</a>. They invoked a principle, later known as the "EPR criterion of reality", positing that: "If, without in any way disturbing a system, we can predict with certainty (i.e., with <a href="/wiki/Probability" title="Probability">probability</a> equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity." From this, they inferred that the second particle must have a definite value of both position and of momentum prior to either quantity being measured. But quantum mechanics considers these two observables <a href="/wiki/Observable#Incompatibility_of_observables_in_quantum_mechanics" title="Observable">incompatible</a> and thus does not associate simultaneous values for both to any system. Einstein, Podolsky, and Rosen therefore concluded that quantum theory does not provide a complete description of reality.<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> In the same year, <a href="/wiki/Erwin_Schr%C3%B6dinger" title="Erwin Schrödinger">Erwin Schrödinger</a> used the word "entanglement" and declared: "I would not call that <i>one</i> but rather <i>the</i> characteristic trait of quantum mechanics."<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> </p><p>The Irish physicist <a href="/wiki/John_Stewart_Bell" title="John Stewart Bell">John Stewart Bell</a> carried the analysis of quantum entanglement much further. He deduced that if measurements are performed independently on the two separated particles of an entangled pair, then the assumption that the outcomes depend upon hidden variables within each half implies a mathematical constraint on how the outcomes on the two measurements are correlated. This constraint would later be named the <a href="/wiki/Bell_inequality" class="mw-redirect" title="Bell inequality">Bell inequality</a>. Bell then showed that quantum physics predicts correlations that violate this inequality. Consequently, the only way that hidden variables could explain the predictions of quantum physics is if they are "nonlocal", which is to say that somehow the two particles are able to interact instantaneously no matter how widely they ever become separated.<sup id="cite_ref-C.B._Parker_1994_542_43-0" class="reference"><a href="#cite_note-C.B._Parker_1994_542-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-ND_Mermin_1993-07_44-0" class="reference"><a href="#cite_note-ND_Mermin_1993-07-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> Performing experiments like those that Bell suggested, physicists have found that nature obeys quantum mechanics and violates Bell inequalities. In other words, the results of these experiments are incompatible with any local hidden variable theory.<sup id="cite_ref-NAT-20180509_45-0" class="reference"><a href="#cite_note-NAT-20180509-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> </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=Introduction_to_quantum_mechanics&action=edit&section=15" title="Edit section: Quantum field theory"><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/Quantum_field_theory" title="Quantum field theory">Quantum field theory</a></div> <p>The idea of quantum field theory began in the late 1920s with British physicist Paul Dirac, when he attempted to <a href="/wiki/Quantization_(physics)" title="Quantization (physics)">quantize</a> the energy of the <a href="/wiki/Electromagnetic_field" title="Electromagnetic field">electromagnetic field</a>; just as in quantum mechanics the energy of an electron in the hydrogen atom was quantized. Quantization is a procedure for constructing a quantum theory starting from a classical theory. </p><p><i><a href="/wiki/Merriam-Webster" title="Merriam-Webster">Merriam-Webster</a></i> defines a <i>field</i> in physics as "a region or space in which a given effect (such as <a href="/wiki/Magnetism" title="Magnetism">magnetism</a>) exists".<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> Other effects that manifest themselves as fields are <a href="/wiki/Gravitation" class="mw-redirect" title="Gravitation">gravitation</a> and <a href="/wiki/Static_electricity" title="Static electricity">static electricity</a>.<sup id="cite_ref-EB-field_48-0" class="reference"><a href="#cite_note-EB-field-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> In 2008, physicist Richard Hammond wrote: </p> <blockquote><p>Sometimes we distinguish between quantum mechanics (QM) and quantum field theory (QFT). QM refers to a system in which the number of particles is fixed, and the fields (such as the electromechanical field) are continuous classical entities. QFT ... goes a step further and allows for the creation and annihilation of particles ...</p></blockquote> <p>He added, however, that <i>quantum mechanics</i> is often used to refer to "the entire notion of quantum view".<sup id="cite_ref-Hammond_49-0" class="reference"><a href="#cite_note-Hammond-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 108">: 108 </span></sup> </p><p>In 1931, Dirac proposed the existence of particles that later became known as <a href="/wiki/Antimatter" title="Antimatter">antimatter</a>.<sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> Dirac shared the <a href="/wiki/Nobel_Prize_in_Physics" title="Nobel Prize in Physics">Nobel Prize in Physics</a> for 1933 with Schrödinger "for the discovery of new productive forms of atomic theory".<sup id="cite_ref-nobel_51-0" class="reference"><a href="#cite_note-nobel-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Quantum_electrodynamics">Quantum electrodynamics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Introduction_to_quantum_mechanics&action=edit&section=16" title="Edit section: Quantum electrodynamics"><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/Quantum_electrodynamics" title="Quantum electrodynamics">Quantum electrodynamics</a></div> <p>Quantum electrodynamics (QED) is the name of the quantum theory of the <a href="/wiki/Electromagnetic_force" class="mw-redirect" title="Electromagnetic force">electromagnetic force</a>. Understanding QED begins with understanding <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetism</a>. Electromagnetism can be called "electrodynamics" because it is a dynamic interaction between electrical and <a href="/wiki/Magnetic_force" class="mw-redirect" title="Magnetic force">magnetic forces</a>. Electromagnetism begins with the <a href="/wiki/Electric_charge" title="Electric charge">electric charge</a>. </p><p>Electric charges are the sources of and create, <a href="/wiki/Electric_field" title="Electric field">electric fields</a>. An electric field is a field that exerts a force on any particles that carry electric charges, at any point in space. This includes the electron, proton, and even <a href="/wiki/Quark" title="Quark">quarks</a>, among others. As a force is exerted, electric charges move, a current flows, and a magnetic field is produced. The changing magnetic field, in turn, causes <a href="/wiki/Electric_current" title="Electric current">electric current</a> (often moving electrons). The physical description of interacting <a href="/wiki/Charged_particle" title="Charged particle">charged particles</a>, electrical currents, electrical fields, and magnetic fields is called electromagnetism. </p><p>In 1928 Paul Dirac produced a relativistic quantum theory of electromagnetism. This was the progenitor to modern quantum electrodynamics, in that it had essential ingredients of the modern theory. However, the problem of unsolvable infinities developed in this <a href="/wiki/Relativistic_quantum_theory" class="mw-redirect" title="Relativistic quantum theory">relativistic quantum theory</a>. Years later, <a href="/wiki/Renormalization" title="Renormalization">renormalization</a> largely solved this problem. Initially viewed as a provisional, suspect procedure by some of its originators, renormalization eventually was embraced as an important and self-consistent tool in QED and other fields of physics. Also, in the late 1940s <a href="/wiki/Feynman_diagram" title="Feynman diagram">Feynman diagrams</a> provided a way to make predictions with QED by finding a probability amplitude for each possible way that an interaction could occur. The diagrams showed in particular that the electromagnetic force is the exchange of photons between interacting particles.<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> </p><p>The <a href="/wiki/Lamb_shift" title="Lamb shift">Lamb shift</a> is an example of a quantum electrodynamics prediction that has been experimentally verified. It is an effect whereby the quantum nature of the electromagnetic field makes the energy levels in an atom or ion deviate slightly from what they would otherwise be. As a result, spectral lines may shift or split. </p><p>Similarly, within a freely propagating electromagnetic wave, the current can also be just an abstract <a href="/wiki/Displacement_current" title="Displacement current">displacement current</a>, instead of involving charge carriers. In QED, its full description makes essential use of short-lived <a href="/wiki/Virtual_particles" class="mw-redirect" title="Virtual particles">virtual particles</a>. There, QED again validates an earlier, rather mysterious concept. </p> <div class="mw-heading mw-heading3"><h3 id="Standard_Model">Standard Model</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Introduction_to_quantum_mechanics&action=edit&section=17" title="Edit section: Standard Model"><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/Standard_Model" title="Standard Model">Standard Model</a></div> <p>The <a href="/wiki/Standard_Model" title="Standard Model">Standard Model</a> of particle physics is the quantum field theory that describes three of the four known <a href="/wiki/Fundamental_force" class="mw-redirect" title="Fundamental force">fundamental forces</a> (<a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetic</a>, <a href="/wiki/Weak_interaction" title="Weak interaction">weak</a> and <a href="/wiki/Strong_interaction" title="Strong interaction">strong interactions</a> – excluding <a href="/wiki/Gravity" title="Gravity">gravity</a>) in the <a href="/wiki/Universe" title="Universe">universe</a> and classifies all known <a href="/wiki/Elementary_particle" title="Elementary particle">elementary particles</a>. It was developed in stages throughout the latter half of the 20th century, through the work of many scientists worldwide, with the current formulation being finalized in the mid-1970s upon <a href="/wiki/Experimental_confirmation" class="mw-redirect" title="Experimental confirmation">experimental confirmation</a> of the existence of <a href="/wiki/Quark" title="Quark">quarks</a>. Since then, proof of the <a href="/wiki/Top_quark" title="Top quark">top quark</a> (1995), the <a href="/wiki/Tau_neutrino" title="Tau neutrino">tau neutrino</a> (2000), and the <a href="/wiki/Higgs_boson" title="Higgs boson">Higgs boson</a> (2012) have added further credence to the Standard Model. In addition, the Standard Model has predicted various properties of <a href="/wiki/Weak_neutral_current" class="mw-redirect" title="Weak neutral current">weak neutral currents</a> and the <a href="/wiki/W_and_Z_bosons" title="W and Z bosons">W and Z bosons</a> with great accuracy. </p><p>Although the Standard Model is believed to be theoretically self-consistent and has demonstrated success in providing <a href="/wiki/Experimental_prediction" class="mw-redirect" title="Experimental prediction">experimental predictions</a>, it leaves some <a href="/wiki/Physics_beyond_the_standard_model" class="mw-redirect" title="Physics beyond the standard model">physical phenomena unexplained</a> and so falls short of being a <a href="/wiki/Theory_of_everything" title="Theory of everything">complete theory of fundamental interactions</a>. For example, it does not fully explain <a href="/wiki/Baryon_asymmetry" title="Baryon asymmetry">baryon asymmetry</a>, incorporate the full <a href="/wiki/Theory_of_gravitation" class="mw-redirect" title="Theory of gravitation">theory of gravitation</a> as described by <a href="/wiki/General_relativity" title="General relativity">general relativity</a>, or account for the <a href="/wiki/Accelerating_expansion_of_the_universe" title="Accelerating expansion of the universe">universe's accelerating expansion</a> as possibly described by <a href="/wiki/Dark_energy" title="Dark energy">dark energy</a>. The model does not contain any viable <a href="/wiki/Dark_matter" title="Dark matter">dark matter</a> particle that possesses all of the required properties deduced from observational <a href="/wiki/Physical_cosmology" title="Physical cosmology">cosmology</a>. It also does not incorporate <a href="/wiki/Neutrino_oscillation" title="Neutrino oscillation">neutrino oscillations</a> and their non-zero masses. Accordingly, it is used as a basis for building more exotic models that incorporate <a href="/wiki/Hypothetical_particle" class="mw-redirect" title="Hypothetical particle">hypothetical particles</a>, <a href="/wiki/Extra_dimensions" title="Extra dimensions">extra dimensions</a>, and elaborate symmetries (such as <a href="/wiki/Supersymmetry" title="Supersymmetry">supersymmetry</a>) to explain experimental results at variance with the Standard Model, such as the existence of dark matter and neutrino oscillations. </p> <div class="mw-heading mw-heading2"><h2 id="Interpretations">Interpretations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Introduction_to_quantum_mechanics&action=edit&section=18" title="Edit section: Interpretations"><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/Interpretations_of_quantum_mechanics" title="Interpretations of quantum mechanics">Interpretations of quantum mechanics</a></div> <p>The physical measurements, equations, and predictions pertinent to quantum mechanics are all consistent and hold a very high level of confirmation. However, the question of what these abstract models say about the underlying nature of the real world has received competing answers. These interpretations are widely varying and sometimes somewhat abstract. For instance, the <a href="/wiki/Copenhagen_interpretation" title="Copenhagen interpretation">Copenhagen interpretation</a> states that before a measurement, statements about a particle's properties are completely meaningless, while the <a href="/wiki/Many-worlds_interpretation" title="Many-worlds interpretation">many-worlds interpretation</a> describes the existence of a <a href="/wiki/Multiverse" title="Multiverse">multiverse</a> made up of every possible universe.<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> </p><p>Light behaves in some aspects like particles and in other aspects like waves. Matter—the "stuff" of the universe consisting of particles such as <a href="/wiki/Electron" title="Electron">electrons</a> and <a href="/wiki/Atom" title="Atom">atoms</a>—exhibits <a href="/wiki/Wave%E2%80%93particle_duality" title="Wave–particle duality">wavelike behavior</a> too. Some light sources, such as <a href="/wiki/Neon_lighting" title="Neon lighting">neon lights</a>, give off only certain specific frequencies of light, a small set of distinct pure colors determined by neon's atomic structure. Quantum mechanics shows that light, along with all other forms of <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic radiation</a>, comes in discrete units, called <a href="/wiki/Photon" title="Photon">photons</a>, and predicts its <a href="/wiki/Spectrum" title="Spectrum">spectral</a> energies (corresponding to pure colors), and the <a href="/wiki/Intensity_(physics)" title="Intensity (physics)">intensities</a> of its light beams. A single photon is a <i><a href="/wiki/Quantum" title="Quantum">quantum</a></i>, or smallest observable particle, of the electromagnetic field. A partial photon is never experimentally observed. More broadly, quantum mechanics shows that many properties of objects, such as position, speed, and <a href="/wiki/Angular_momentum" title="Angular momentum">angular momentum</a>, that appeared continuous in the zoomed-out view of classical mechanics, turn out to be (in the very tiny, zoomed-in scale of quantum mechanics) <i><a href="/wiki/Quantization_(physics)" title="Quantization (physics)">quantized</a></i>. Such properties of <a href="/wiki/Elementary_particles" class="mw-redirect" title="Elementary particles">elementary particles</a> are required to take on one of a set of small, discrete allowable values, and since the gap between these values is also small, the discontinuities are only apparent at very tiny (atomic) scales. </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Introduction_to_quantum_mechanics&action=edit&section=19" title="Edit section: Applications"><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/Applications_of_quantum_mechanics" title="Applications of quantum mechanics">Applications of quantum mechanics</a></div> <div class="mw-heading mw-heading3"><h3 id="Everyday_applications">Everyday applications</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Introduction_to_quantum_mechanics&action=edit&section=20" title="Edit section: Everyday applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The relationship between the frequency of electromagnetic radiation and the energy of each photon is why <a href="/wiki/Ultraviolet" title="Ultraviolet">ultraviolet</a> light can cause <a href="/wiki/Sunburn" title="Sunburn">sunburn</a>, but visible or <a href="/wiki/Infrared" title="Infrared">infrared</a> light cannot. A photon of ultraviolet light delivers a high amount of <a href="/wiki/Energy" title="Energy">energy</a>—enough to contribute to cellular damage such as occurs in a sunburn. A photon of infrared light delivers less energy—only enough to warm one's skin. So, an infrared lamp can warm a large surface, perhaps large enough to keep people comfortable in a cold room, but it cannot give anyone a sunburn.<sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Technological_applications">Technological applications</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Introduction_to_quantum_mechanics&action=edit&section=21" title="Edit section: Technological applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Applications of quantum mechanics include the <a href="/wiki/Laser" title="Laser">laser</a>, the <a href="/wiki/Transistor" title="Transistor">transistor</a>, the <a href="/wiki/Electron_microscope" title="Electron microscope">electron microscope</a>, and <a href="/wiki/Magnetic_Resonance_Imaging" class="mw-redirect" title="Magnetic Resonance Imaging">magnetic resonance imaging</a>. A special class of quantum mechanical applications is related to <a href="/wiki/Macroscopic_quantum_phenomena" title="Macroscopic quantum phenomena">macroscopic quantum phenomena</a> such as superfluid helium and superconductors. The study of semiconductors led to the invention of the <a href="/wiki/Diode" title="Diode">diode</a> and the <a href="/wiki/Transistor" title="Transistor">transistor</a>, which are indispensable for modern <a href="/wiki/Electronics" title="Electronics">electronics</a>. </p><p>In even a simple <a href="/wiki/Light_switch" title="Light switch">light switch</a>, <a href="/wiki/Quantum_tunneling" class="mw-redirect" title="Quantum tunneling">quantum tunneling</a> is absolutely vital, as otherwise the electrons in the <a href="/wiki/Electric_current" title="Electric current">electric current</a> could not penetrate the potential barrier made up of a layer of oxide. <a href="/wiki/Flash_memory" title="Flash memory">Flash memory</a> chips found in <a href="/wiki/USB_flash_drive" title="USB flash drive">USB drives</a> also use quantum tunneling, to erase their memory cells.<sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> </p> <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=Introduction_to_quantum_mechanics&action=edit&section=22" 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 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srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/37px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/49px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 2x" data-file-width="530" data-file-height="600" /></a></span></span><span class="portalbox-link"><a href="/wiki/Portal:Physics" title="Portal:Physics">Physics portal</a></span></li></ul> <ul><li><a href="/wiki/Einstein%27s_thought_experiments" title="Einstein's thought experiments">Einstein's thought experiments</a></li> <li><a href="/wiki/Macroscopic_quantum_phenomena" title="Macroscopic quantum phenomena">Macroscopic quantum phenomena</a></li> <li><a href="/wiki/Philosophy_of_physics" title="Philosophy of physics">Philosophy of physics</a></li> <li><a href="/wiki/Quantum_computing" title="Quantum computing">Quantum computing</a></li> <li><a href="/wiki/Virtual_particle" title="Virtual particle">Virtual particle</a></li> <li><a href="/wiki/Teaching_quantum_mechanics" title="Teaching quantum mechanics">Teaching quantum mechanics</a></li> <li><a href="/wiki/List_of_textbooks_on_classical_mechanics_and_quantum_mechanics" title="List of textbooks on classical mechanics and quantum mechanics">List of textbooks on classical and quantum mechanics</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Introduction_to_quantum_mechanics&action=edit&section=23" title="Edit section: Notes"><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"> </div> <p>Notes are in the main script </p> <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=Introduction_to_quantum_mechanics&action=edit&section=24" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.pbs.org/transistor/science/info/quantum.html">"Quantum Mechanics"</a>. <a href="/wiki/National_Public_Radio" class="mw-redirect" title="National Public Radio">National Public Radio</a><span class="reference-accessdate">. Retrieved <span class="nowrap">22 June</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Quantum+Mechanics&rft.pub=National+Public+Radio&rft_id=https%3A%2F%2Fwww.pbs.org%2Ftransistor%2Fscience%2Finfo%2Fquantum.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+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">Kuhn, Thomas S. <i>The Structure of Scientific Revolutions</i>. Fourth ed. Chicago; London: The University of Chicago Press, 2012. Print.</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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20170915203853/https://www.socratease.in/chapters/intro/intro-to-quantum-mechanics-1">"Introduction to Quantum Mechanics"</a>. <i>Socratease</i>. Archived from <a rel="nofollow" class="external text" href="https://www.socratease.in/chapters/intro/intro-to-quantum-mechanics-1">the original</a> on 15 September 2017.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Socratease&rft.atitle=Introduction+to+Quantum+Mechanics&rft_id=https%3A%2F%2Fwww.socratease.in%2Fchapters%2Fintro%2Fintro-to-quantum-mechanics-1&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+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="CITEREFFeynman1988" class="citation book cs1">Feynman, Richard P. (1988). <a rel="nofollow" class="external text" href="https://archive.org/details/qedstrangetheory00feyn/page/10"><i>QED : the strange theory of light and matter</i></a> (1st Princeton pbk., seventh printing with corrections. ed.). Princeton, NJ: Princeton University Press. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/qedstrangetheory00feyn/page/10">10</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0691024172" title="Special:BookSources/978-0691024172"><bdi>978-0691024172</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=QED+%3A+the+strange+theory+of+light+and+matter&rft.place=Princeton%2C+NJ&rft.pages=10&rft.edition=1st+Princeton+pbk.%2C+seventh+printing+with+corrections.&rft.pub=Princeton+University+Press&rft.date=1988&rft.isbn=978-0691024172&rft.aulast=Feynman&rft.aufirst=Richard+P.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fqedstrangetheory00feyn%2Fpage%2F10&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-Whittaker-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-Whittaker_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Whittaker_5-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Whittaker_5-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><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+%E2%80%93+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%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-Baggott-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-Baggott_6-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Baggott_6-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Baggott_6-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Baggott_6-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-Baggott_6-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-Baggott_6-5"><sup><i><b>f</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBaggott2013" class="citation book cs1">Baggott, J. E. (2013). <i>The quantum story: a history in 40 moments</i> (Impression: 3 ed.). Oxford: Oxford Univ. Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-965597-7" title="Special:BookSources/978-0-19-965597-7"><bdi>978-0-19-965597-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+quantum+story%3A+a+history+in+40+moments&rft.place=Oxford&rft.edition=Impression%3A+3&rft.pub=Oxford+Univ.+Press&rft.date=2013&rft.isbn=978-0-19-965597-7&rft.aulast=Baggott&rft.aufirst=J.+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+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="CITEREFMillikan1916" class="citation journal cs1">Millikan, R. A. (1 March 1916). <a rel="nofollow" class="external text" href="https://link.aps.org/doi/10.1103/PhysRev.7.355">"A Direct Photoelectric Determination of Planck's " h "<span class="cs1-kern-right"></span>"</a>. <i>Physical Review</i>. <b>7</b> (3): 355–388. <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/1916PhRv....7..355M">1916PhRv....7..355M</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%2FPhysRev.7.355">10.1103/PhysRev.7.355</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/0031-899X">0031-899X</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&rft.atitle=A+Direct+Photoelectric+Determination+of+Planck%27s+%22+h+%22&rft.volume=7&rft.issue=3&rft.pages=355-388&rft.date=1916-03-01&rft.issn=0031-899X&rft_id=info%3Adoi%2F10.1103%2FPhysRev.7.355&rft_id=info%3Abibcode%2F1916PhRv....7..355M&rft.aulast=Millikan&rft.aufirst=R.+A.&rft_id=https%3A%2F%2Flink.aps.org%2Fdoi%2F10.1103%2FPhysRev.7.355&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-pais-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-pais_8-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPais1979" class="citation journal cs1">Pais, A. (1 October 1979). <a rel="nofollow" class="external text" href="https://link.aps.org/doi/10.1103/RevModPhys.51.863">"Einstein and the quantum theory"</a>. <i>Reviews of Modern Physics</i>. <b>51</b> (4): 863–914. <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/1979RvMP...51..863P">1979RvMP...51..863P</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%2FRevModPhys.51.863">10.1103/RevModPhys.51.863</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/0034-6861">0034-6861</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Reviews+of+Modern+Physics&rft.atitle=Einstein+and+the+quantum+theory&rft.volume=51&rft.issue=4&rft.pages=863-914&rft.date=1979-10-01&rft.issn=0034-6861&rft_id=info%3Adoi%2F10.1103%2FRevModPhys.51.863&rft_id=info%3Abibcode%2F1979RvMP...51..863P&rft.aulast=Pais&rft.aufirst=A.&rft_id=https%3A%2F%2Flink.aps.org%2Fdoi%2F10.1103%2FRevModPhys.51.863&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-messiah-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-messiah_9-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMessiah1966" class="citation book cs1">Messiah, Albert (1966). <i>Quantum Mechanics</i>. North Holland, John Wiley & Sons. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0486409244" title="Special:BookSources/0486409244"><bdi>0486409244</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+Mechanics&rft.pub=North+Holland%2C+John+Wiley+%26+Sons&rft.date=1966&rft.isbn=0486409244&rft.aulast=Messiah&rft.aufirst=Albert&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+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="https://web.archive.org/web/20210710112443/https://www.reed.edu/physics/faculty/wheeler/documents/Quantum%20Mechanics/Miscellaneous%20Essays/Ehrenfest's%20Theorem.pdf">"Remarks concerning the status & some ramifications of EHRENFEST'S THEOREM"</a> <span class="cs1-format">(PDF)</span>. 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"Matter–wave interference of particles selected from a molecular library with masses exceeding 10 000 amu". <i>Physical Chemistry Chemical Physics</i>. <b>15</b> (35): 14696–700. <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/1310.8343">1310.8343</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/2013PCCP...1514696E">2013PCCP...1514696E</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1039%2FC3CP51500A">10.1039/C3CP51500A</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/23900710">23900710</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:3944699">3944699</a>. <q>[I]n a three-grating interferometer... We observe high-contrast quantum fringe patterns of molecules... having 810 atoms in a single particle.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Chemistry+Chemical+Physics&rft.atitle=Matter%E2%80%93wave+interference+of+particles+selected+from+a+molecular+library+with+masses+exceeding+10+000+amu&rft.volume=15&rft.issue=35&rft.pages=14696-700&rft.date=2013&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A3944699%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2013PCCP...1514696E&rft_id=info%3Aarxiv%2F1310.8343&rft_id=info%3Apmid%2F23900710&rft_id=info%3Adoi%2F10.1039%2FC3CP51500A&rft.aulast=Eibenberger&rft.aufirst=Sandra&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</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.nobelprize.org/prizes/physics/1932/summary/">"The Nobel Prize in Physics 1932"</a>. <i>NobelPrize.org</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=NobelPrize.org&rft.atitle=The+Nobel+Prize+in+Physics+1932&rft_id=https%3A%2F%2Fwww.nobelprize.org%2Fprizes%2Fphysics%2F1932%2Fsummary%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-36">^</a></b></span> <span class="reference-text">Heisenberg first published his work on the uncertainty principle in the leading German physics journal <i>Zeitschrift für Physik</i>: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHeisenberg1927" class="citation journal cs1">Heisenberg, W. (1927). "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik". <i>Z. Phys</i>. <b>43</b> (3–4): 172–98. <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/1927ZPhy...43..172H">1927ZPhy...43..172H</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%2FBF01397280">10.1007/BF01397280</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:122763326">122763326</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Z.+Phys.&rft.atitle=%C3%9Cber+den+anschaulichen+Inhalt+der+quantentheoretischen+Kinematik+und+Mechanik&rft.volume=43&rft.issue=3%E2%80%934&rft.pages=172-98&rft.date=1927&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A122763326%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2FBF01397280&rft_id=info%3Abibcode%2F1927ZPhy...43..172H&rft.aulast=Heisenberg&rft.aufirst=W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></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"><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.nobelprize.org/prizes/physics/1932/ceremony-speech/">"The Nobel Prize in Physics 1932"</a>. <i>NobelPrize.org</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=NobelPrize.org&rft.atitle=The+Nobel+Prize+in+Physics+1932&rft_id=https%3A%2F%2Fwww.nobelprize.org%2Fprizes%2Fphysics%2F1932%2Fceremony-speech%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-EB-uncertainty-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-EB-uncertainty_38-0">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.britannica.com/EBchecked/topic/614029/uncertainty-principle">"Uncertainty principle", <i>Encyclopædia Britannica</i></a></span> </li> <li id="cite_note-Pauling-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-Pauling_39-0">^</a></b></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%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-EPR-40"><span class="mw-cite-backlink"><b><a href="#cite_ref-EPR_40-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEinsteinB_PodolskyN_Rosen1935" class="citation journal cs1">Einstein, A; B Podolsky; N Rosen (15 May 1935). <a rel="nofollow" class="external text" href="https://cds.cern.ch/record/405662/files/PhysRev.47.777.pdf">"Can Quantum-Mechanical Description of Physical Reality be Considered Complete?"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/Physical_Review" title="Physical Review">Physical Review</a></i>. <b>47</b> (10): 777–780. <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/1935PhRv...47..777E">1935PhRv...47..777E</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/10.1103%2FPhysRev.47.777">10.1103/PhysRev.47.777</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review&rft.atitle=Can+Quantum-Mechanical+Description+of+Physical+Reality+be+Considered+Complete%3F&rft.volume=47&rft.issue=10&rft.pages=777-780&rft.date=1935-05-15&rft_id=info%3Adoi%2F10.1103%2FPhysRev.47.777&rft_id=info%3Abibcode%2F1935PhRv...47..777E&rft.aulast=Einstein&rft.aufirst=A&rft.au=B+Podolsky&rft.au=N+Rosen&rft_id=https%3A%2F%2Fcds.cern.ch%2Frecord%2F405662%2Ffiles%2FPhysRev.47.777.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-41"><span class="mw-cite-backlink"><b><a href="#cite_ref-41">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPeres2002" class="citation book cs1"><a href="/wiki/Asher_Peres" title="Asher Peres">Peres, Asher</a> (2002). <a href="/wiki/Quantum_Theory:_Concepts_and_Methods" title="Quantum Theory: Concepts and Methods"><i>Quantum Theory: Concepts and Methods</i></a>. Kluwer. p. 149.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Theory%3A+Concepts+and+Methods&rft.pages=149&rft.pub=Kluwer&rft.date=2002&rft.aulast=Peres&rft.aufirst=Asher&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-42"><span class="mw-cite-backlink"><b><a href="#cite_ref-42">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchrödinger1935" class="citation journal cs1">Schrödinger, E. (1935). "Discussion of probability relations between separated systems". <i>Proceedings of the Cambridge Philosophical Society</i>. <b>31</b> (4): 555. <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/1935PCPS...31..555S">1935PCPS...31..555S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FS0305004100013554">10.1017/S0305004100013554</a>. <q>When two systems, of which we know the states by their respective representation, enter into a temporary physical interaction due to known forces between them and when after a time of mutual influence the systems separate again, then they can no longer be described as before, viz., by endowing each of them with a representative of its own. I would not call that <i>one</i> but rather <i>the</i> characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+Cambridge+Philosophical+Society&rft.atitle=Discussion+of+probability+relations+between+separated+systems&rft.volume=31&rft.issue=4&rft.pages=555&rft.date=1935&rft_id=info%3Adoi%2F10.1017%2FS0305004100013554&rft_id=info%3Abibcode%2F1935PCPS...31..555S&rft.aulast=Schr%C3%B6dinger&rft.aufirst=E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-C.B._Parker_1994_542-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-C.B._Parker_1994_542_43-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFParker1994" class="citation book cs1">Parker, Sybil B. (1994). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/mcgrawhillencycl1993park"><i>McGraw-Hill Encyclopaedia of Physics</i></a></span> (2nd ed.). McGraw-Hill. p. <a rel="nofollow" class="external text" href="https://archive.org/details/mcgrawhillencycl1993park/page/542">542</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-051400-3" title="Special:BookSources/978-0-07-051400-3"><bdi>978-0-07-051400-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=McGraw-Hill+Encyclopaedia+of+Physics&rft.pages=542&rft.edition=2nd&rft.pub=McGraw-Hill&rft.date=1994&rft.isbn=978-0-07-051400-3&rft.aulast=Parker&rft.aufirst=Sybil+B.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmcgrawhillencycl1993park&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-ND_Mermin_1993-07-44"><span class="mw-cite-backlink"><b><a href="#cite_ref-ND_Mermin_1993-07_44-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMermin1993" class="citation journal cs1"><a href="/wiki/N._David_Mermin" title="N. 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A. K.; Ahmed, H. (2008). Vijay Kumar (ed.). <i>Nanosilicon</i>. Elsevier. p. 345. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0080445281" title="Special:BookSources/978-0080445281"><bdi>978-0080445281</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Nanosilicon&rft.pages=345&rft.pub=Elsevier&rft.date=2008&rft.isbn=978-0080445281&rft.aulast=Durrani&rft.aufirst=Z.+A.+K.&rft.au=Ahmed%2C+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Bibliography">Bibliography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Introduction_to_quantum_mechanics&action=edit&section=25" title="Edit section: Bibliography"><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="CITEREFBernstein2005" class="citation journal cs1">Bernstein, Jeremy (2005). <a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.2060717">"Max Born and the quantum theory"</a>. <i><a href="/wiki/American_Journal_of_Physics" title="American Journal of Physics">American Journal of Physics</a></i>. <b>73</b> (11): 999–1008. <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/2005AmJPh..73..999B">2005AmJPh..73..999B</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/10.1119%2F1.2060717">10.1119/1.2060717</a></span>.</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=Max+Born+and+the+quantum+theory&rft.volume=73&rft.issue=11&rft.pages=999-1008&rft.date=2005&rft_id=info%3Adoi%2F10.1119%2F1.2060717&rft_id=info%3Abibcode%2F2005AmJPh..73..999B&rft.aulast=Bernstein&rft.aufirst=Jeremy&rft_id=https%3A%2F%2Fdoi.org%2F10.1119%252F1.2060717&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBeller2001" class="citation book cs1">Beller, Mara (2001). <i>Quantum Dialogue: The Making of a Revolution</i>. 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Noonday Press. <a href="/wiki/LCCN_(identifier)" class="mw-redirect" title="LCCN (identifier)">LCCN</a> <a rel="nofollow" class="external text" href="https://lccn.loc.gov/53010401">53010401</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Revolution+in+Physics&rft.pub=Noonday+Press&rft.date=1953&rft_id=info%3Alccn%2F53010401&rft.aulast=de+Broglie&rft.aufirst=Louis&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBronnerStrunzSilberhornMeyn2009" class="citation journal cs1">Bronner, Patrick; Strunz, Andreas; Silberhorn, Christine; Meyn, Jan-Peter (2009). "Demonstrating quantum random with single photons". <i>European Journal of Physics</i>. <b>30</b> (5): 1189–1200. <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/2009EJPh...30.1189B">2009EJPh...30.1189B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F0143-0807%2F30%2F5%2F026">10.1088/0143-0807/30/5/026</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:7903179">7903179</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=European+Journal+of+Physics&rft.atitle=Demonstrating+quantum+random+with+single+photons&rft.volume=30&rft.issue=5&rft.pages=1189-1200&rft.date=2009&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A7903179%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1088%2F0143-0807%2F30%2F5%2F026&rft_id=info%3Abibcode%2F2009EJPh...30.1189B&rft.aulast=Bronner&rft.aufirst=Patrick&rft.au=Strunz%2C+Andreas&rft.au=Silberhorn%2C+Christine&rft.au=Meyn%2C+Jan-Peter&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEinstein1934" class="citation book cs1"><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein, Albert</a> (1934). <i>Essays in Science</i>. <a href="/wiki/Philosophical_Library" title="Philosophical Library">Philosophical Library</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0486470113" title="Special:BookSources/0486470113"><bdi>0486470113</bdi></a>. <a href="/wiki/LCCN_(identifier)" class="mw-redirect" title="LCCN (identifier)">LCCN</a> <a rel="nofollow" class="external text" href="https://lccn.loc.gov/55003947">55003947</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Essays+in+Science&rft.pub=Philosophical+Library&rft.date=1934&rft_id=info%3Alccn%2F55003947&rft.isbn=0486470113&rft.aulast=Einstein&rft.aufirst=Albert&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFeiglBrodbeck1953" class="citation book cs1"><a href="/wiki/Herbert_Feigl" title="Herbert Feigl">Feigl, Herbert</a>; <a href="/wiki/May_Brodbeck" title="May Brodbeck">Brodbeck, May</a> (1953). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/readingsinphilos00feig"><i>Readings in the Philosophy of Science</i></a></span>. Appleton-Century-Crofts. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0390304883" title="Special:BookSources/0390304883"><bdi>0390304883</bdi></a>. <a href="/wiki/LCCN_(identifier)" class="mw-redirect" title="LCCN (identifier)">LCCN</a> <a rel="nofollow" class="external text" href="https://lccn.loc.gov/53006438">53006438</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Readings+in+the+Philosophy+of+Science&rft.pub=Appleton-Century-Crofts&rft.date=1953&rft_id=info%3Alccn%2F53006438&rft.isbn=0390304883&rft.aulast=Feigl&rft.aufirst=Herbert&rft.au=Brodbeck%2C+May&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Freadingsinphilos00feig&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFeynman1949" class="citation journal cs1"><a href="/wiki/Richard_Feynman" title="Richard Feynman">Feynman, Richard P.</a> (1949). <a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRev.76.769">"Space-Time Approach to Quantum Electrodynamics"</a>. <i><a href="/wiki/Physical_Review" title="Physical Review">Physical Review</a></i>. <b>76</b> (6): 769–89. <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/1949PhRv...76..769F">1949PhRv...76..769F</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/10.1103%2FPhysRev.76.769">10.1103/PhysRev.76.769</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review&rft.atitle=Space-Time+Approach+to+Quantum+Electrodynamics&rft.volume=76&rft.issue=6&rft.pages=769-89&rft.date=1949&rft_id=info%3Adoi%2F10.1103%2FPhysRev.76.769&rft_id=info%3Abibcode%2F1949PhRv...76..769F&rft.aulast=Feynman&rft.aufirst=Richard+P.&rft_id=https%3A%2F%2Fdoi.org%2F10.1103%252FPhysRev.76.769&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFeynman1990" class="citation book cs1"><a href="/wiki/Richard_Feynman" title="Richard Feynman">Feynman, Richard P.</a> (1990). <i>QED, The Strange Theory of Light and Matter</i>. Penguin Books. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0140125054" title="Special:BookSources/978-0140125054"><bdi>978-0140125054</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=QED%2C+The+Strange+Theory+of+Light+and+Matter&rft.pub=Penguin+Books&rft.date=1990&rft.isbn=978-0140125054&rft.aulast=Feynman&rft.aufirst=Richard+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFowler1999" class="citation book cs1">Fowler, Michael (1999). <a rel="nofollow" class="external text" href="https://galileo.phys.virginia.edu/classes/252/Bohr_Atom/Bohr_Atom.html"><i>The Bohr Atom</i></a>. University of Virginia.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Bohr+Atom&rft.pub=University+of+Virginia&rft.date=1999&rft.aulast=Fowler&rft.aufirst=Michael&rft_id=https%3A%2F%2Fgalileo.phys.virginia.edu%2Fclasses%2F252%2FBohr_Atom%2FBohr_Atom.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="Please supply an ISBN for this book.">ISBN missing</span></a></i>]</sup></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHeisenberg1958" class="citation book cs1"><a href="/wiki/Werner_Heisenberg" title="Werner Heisenberg">Heisenberg, Werner</a> (1958). <a rel="nofollow" class="external text" href="https://archive.org/details/physicsphilosoph00heis"><i>Physics and Philosophy</i></a>. Harper and Brothers. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0061305499" title="Special:BookSources/0061305499"><bdi>0061305499</bdi></a>. <a href="/wiki/LCCN_(identifier)" class="mw-redirect" title="LCCN (identifier)">LCCN</a> <a rel="nofollow" class="external text" href="https://lccn.loc.gov/99010404">99010404</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physics+and+Philosophy&rft.pub=Harper+and+Brothers&rft.date=1958&rft_id=info%3Alccn%2F99010404&rft.isbn=0061305499&rft.aulast=Heisenberg&rft.aufirst=Werner&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fphysicsphilosoph00heis&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLakshmibala2004" class="citation journal cs1">Lakshmibala, S. (2004). "Heisenberg, Matrix Mechanics and the Uncertainty Principle". <i><a href="/wiki/Resonance:_Journal_of_Science_Education" class="mw-redirect" title="Resonance: Journal of Science Education">Resonance: Journal of Science Education</a></i>. <b>9</b> (8): 46–56. <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%2Fbf02837577">10.1007/bf02837577</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:29893512">29893512</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Resonance%3A+Journal+of+Science+Education&rft.atitle=Heisenberg%2C+Matrix+Mechanics+and+the+Uncertainty+Principle&rft.volume=9&rft.issue=8&rft.pages=46-56&rft.date=2004&rft_id=info%3Adoi%2F10.1007%2Fbf02837577&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A29893512%23id-name%3DS2CID&rft.aulast=Lakshmibala&rft.aufirst=S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLiboff1992" class="citation book cs1"><a href="/wiki/Richard_Liboff" title="Richard Liboff">Liboff, Richard L.</a> (1992). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/introductoryquan00libo"><i>Introductory Quantum Mechanics</i></a></span> (2nd ed.). Addison-Wesley Pub. Co. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780201547153" title="Special:BookSources/9780201547153"><bdi>9780201547153</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introductory+Quantum+Mechanics&rft.edition=2nd&rft.pub=Addison-Wesley+Pub.+Co.&rft.date=1992&rft.isbn=9780201547153&rft.aulast=Liboff&rft.aufirst=Richard+L.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fintroductoryquan00libo&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="Please supply an ISBN for this book.">ISBN missing</span></a></i>]</sup></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLindsayMargenau1957" class="citation book cs1">Lindsay, Robert Bruce; Margenau, Henry (1957). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/foundationsofphy00lind"><i>Foundations of Physics</i></a></span>. Dover. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0918024188" title="Special:BookSources/0918024188"><bdi>0918024188</bdi></a>. <a href="/wiki/LCCN_(identifier)" class="mw-redirect" title="LCCN (identifier)">LCCN</a> <a rel="nofollow" class="external text" href="https://lccn.loc.gov/57014416">57014416</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Foundations+of+Physics&rft.pub=Dover&rft.date=1957&rft_id=info%3Alccn%2F57014416&rft.isbn=0918024188&rft.aulast=Lindsay&rft.aufirst=Robert+Bruce&rft.au=Margenau%2C+Henry&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Ffoundationsofphy00lind&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcEvoyZarate2004" class="citation book cs1">McEvoy, J. P.; Zarate, Oscar (2004). <a rel="nofollow" class="external text" href="https://archive.org/details/introducingquant00mcev"><i>Introducing Quantum Theory</i></a>. Icon Books. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1874166374" title="Special:BookSources/1874166374"><bdi>1874166374</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.pub=Icon+Books&rft.date=2004&rft.isbn=1874166374&rft.aulast=McEvoy&rft.aufirst=J.+P.&rft.au=Zarate%2C+Oscar&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fintroducingquant00mcev&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNave2005" class="citation web cs1">Nave, Carl Rod (2005). <a rel="nofollow" class="external text" href="http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon">"Quantum Physics"</a>. <i><a href="/wiki/HyperPhysics" title="HyperPhysics">HyperPhysics</a></i>. Georgia State University.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=HyperPhysics&rft.atitle=Quantum+Physics&rft.date=2005&rft.aulast=Nave&rft.aufirst=Carl+Rod&rft_id=http%3A%2F%2Fhyperphysics.phy-astr.gsu.edu%2Fhbase%2Fquacon.html%23quacon&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPeat2002" class="citation book cs1">Peat, F. David (2002). <i>From Certainty to Uncertainty: The Story of Science and Ideas in the Twenty-First Century</i>. <a href="/wiki/Joseph_Henry_Press" title="Joseph Henry Press">Joseph Henry Press</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=From+Certainty+to+Uncertainty%3A+The+Story+of+Science+and+Ideas+in+the+Twenty-First+Century&rft.pub=Joseph+Henry+Press&rft.date=2002&rft.aulast=Peat&rft.aufirst=F.+David&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFReichenbach1944" class="citation book cs1"><a href="/wiki/Hans_Reichenbach" title="Hans Reichenbach">Reichenbach, Hans</a> (1944). <a rel="nofollow" class="external text" href="https://archive.org/details/in.ernet.dli.2015.212027"><i>Philosophic Foundations of Quantum Mechanics</i></a>. University of California Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0486404595" title="Special:BookSources/0486404595"><bdi>0486404595</bdi></a>. <a href="/wiki/LCCN_(identifier)" class="mw-redirect" title="LCCN (identifier)">LCCN</a> <a rel="nofollow" class="external text" href="https://lccn.loc.gov/a44004471">a44004471</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Philosophic+Foundations+of+Quantum+Mechanics&rft.pub=University+of+California+Press&rft.date=1944&rft_id=info%3Alccn%2Fa44004471&rft.isbn=0486404595&rft.aulast=Reichenbach&rft.aufirst=Hans&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fin.ernet.dli.2015.212027&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchilpp1949" class="citation book cs1"><a href="/wiki/Paul_Arthur_Schilpp" title="Paul Arthur Schilpp">Schilpp, Paul Arthur</a> (1949). <i>Albert Einstein: Philosopher-Scientist</i>. Tudor Publishing Company. <a href="/wiki/LCCN_(identifier)" class="mw-redirect" title="LCCN (identifier)">LCCN</a> <a rel="nofollow" class="external text" href="https://lccn.loc.gov/50005340">50005340</a>.</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+Philosopher-Scientist&rft.pub=Tudor+Publishing+Company&rft.date=1949&rft_id=info%3Alccn%2F50005340&rft.aulast=Schilpp&rft.aufirst=Paul+Arthur&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></li> <li><i>Scientific American Reader</i>, 1953.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSears1949" class="citation book cs1"><a href="/w/index.php?title=F._W._Sears&action=edit&redlink=1" class="new" title="F. W. Sears (page does not exist)">Sears, Francis Weston</a> (1949). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/neutronopticsint0000sear"><i>Optics</i></a></span> (3rd ed.). Addison-Wesley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0195046013" title="Special:BookSources/0195046013"><bdi>0195046013</bdi></a>. <a href="/wiki/LCCN_(identifier)" class="mw-redirect" title="LCCN (identifier)">LCCN</a> <a rel="nofollow" class="external text" href="https://lccn.loc.gov/51001018">51001018</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Optics&rft.edition=3rd&rft.pub=Addison-Wesley&rft.date=1949&rft_id=info%3Alccn%2F51001018&rft.isbn=0195046013&rft.aulast=Sears&rft.aufirst=Francis+Weston&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fneutronopticsint0000sear&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShimony1983" class="citation conference cs1"><a href="/wiki/Abner_Shimony" title="Abner Shimony">Shimony, A.</a> (1983). "(title not given in citation)". <i>Foundations of Quantum Mechanics in the Light of New Technology (S. Kamefuchi et al., eds.)</i>. Tokyo: Japan Physical Society. p. 225.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.atitle=%28title+not+given+in+citation%29&rft.btitle=Foundations+of+Quantum+Mechanics+in+the+Light+of+New+Technology+%28S.+Kamefuchi+et+al.%2C+eds.%29&rft.place=Tokyo&rft.pages=225&rft.pub=Japan+Physical+Society&rft.date=1983&rft.aulast=Shimony&rft.aufirst=A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span>; cited in: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPopescuDaniel_Rohrlich1996" class="citation arxiv cs1">Popescu, Sandu; Daniel Rohrlich (1996). "Action and Passion at a Distance: An Essay in Honor of Professor Abner Shimony". <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/9605004">quant-ph/9605004</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=Action+and+Passion+at+a+Distance%3A+An+Essay+in+Honor+of+Professor+Abner+Shimony&rft.date=1996&rft_id=info%3Aarxiv%2Fquant-ph%2F9605004&rft.aulast=Popescu&rft.aufirst=Sandu&rft.au=Daniel+Rohrlich&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTavelTavel2002" class="citation book cs1">Tavel, Morton; Tavel, Judith (illustrations) (2002). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=SELS0HbIhjYC&q=Wave+function+collapse&pg=PA200"><i>Contemporary physics and the limits of knowledge</i></a>. Rutgers University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0813530772" title="Special:BookSources/978-0813530772"><bdi>978-0813530772</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Contemporary+physics+and+the+limits+of+knowledge&rft.pub=Rutgers+University+Press&rft.date=2002&rft.isbn=978-0813530772&rft.aulast=Tavel&rft.aufirst=Morton&rft.au=Tavel%2C+Judith+%28illustrations%29&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DSELS0HbIhjYC%26q%3DWave%2Bfunction%2Bcollapse%26pg%3DPA200&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></li> <li>Van Vleck, J. H.,1928, "The Correspondence Principle in the Statistical Interpretation of Quantum Mechanics", <i>Proc. Natl. Acad. Sci.</i> 14: 179.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWestmorelandBenjamin_Schumacher1998" class="citation arxiv cs1">Westmoreland; Benjamin Schumacher (1998). "Quantum Entanglement and the Nonexistence of Superluminal Signals". <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/9801014">quant-ph/9801014</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=Quantum+Entanglement+and+the+Nonexistence+of+Superluminal+Signals&rft.date=1998&rft_id=info%3Aarxiv%2Fquant-ph%2F9801014&rft.au=Westmoreland&rft.au=Benjamin+Schumacher&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWheelerFeynman1949" class="citation journal cs1"><a href="/wiki/John_Archibald_Wheeler" title="John Archibald Wheeler">Wheeler, John Archibald</a>; <a href="/wiki/Richard_Feynman" title="Richard Feynman">Feynman, Richard P.</a> (1949). <a rel="nofollow" class="external text" href="https://cds.cern.ch/record/1062647/files/RevModPhys.21.425.pdf">"Classical Electrodynamics in Terms of Direct Interparticle Action"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/Reviews_of_Modern_Physics" title="Reviews of Modern Physics">Reviews of Modern Physics</a></i>. <b>21</b> (3): 425–33. <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/1949RvMP...21..425W">1949RvMP...21..425W</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/10.1103%2FRevModPhys.21.425">10.1103/RevModPhys.21.425</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Reviews+of+Modern+Physics&rft.atitle=Classical+Electrodynamics+in+Terms+of+Direct+Interparticle+Action&rft.volume=21&rft.issue=3&rft.pages=425-33&rft.date=1949&rft_id=info%3Adoi%2F10.1103%2FRevModPhys.21.425&rft_id=info%3Abibcode%2F1949RvMP...21..425W&rft.aulast=Wheeler&rft.aufirst=John+Archibald&rft.au=Feynman%2C+Richard+P.&rft_id=https%3A%2F%2Fcds.cern.ch%2Frecord%2F1062647%2Ffiles%2FRevModPhys.21.425.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWiemanPerkins2005" class="citation journal cs1">Wieman, Carl; Perkins, Katherine (2005). "Transforming Physics Education". <i><a href="/wiki/Physics_Today" title="Physics Today">Physics Today</a></i>. <b>58</b> (11): 36. <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/2005PhT....58k..36W">2005PhT....58k..36W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.2155756">10.1063/1.2155756</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Today&rft.atitle=Transforming+Physics+Education&rft.volume=58&rft.issue=11&rft.pages=36&rft.date=2005&rft_id=info%3Adoi%2F10.1063%2F1.2155756&rft_id=info%3Abibcode%2F2005PhT....58k..36W&rft.aulast=Wieman&rft.aufirst=Carl&rft.au=Perkins%2C+Katherine&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></li></ul> <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=Introduction_to_quantum_mechanics&action=edit&section=26" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Update plainlinks metadata ambox ambox-content ambox-Update" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Ambox_current_red_Americas.svg/42px-Ambox_current_red_Americas.svg.png" decoding="async" width="42" height="34" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Ambox_current_red_Americas.svg/63px-Ambox_current_red_Americas.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/53/Ambox_current_red_Americas.svg/84px-Ambox_current_red_Americas.svg.png 2x" data-file-width="360" data-file-height="290" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section needs to be <b>updated</b>.<span class="hide-when-compact"> Please help update this article to reflect recent events or newly available information.</span> <span class="date-container"><i>(<span class="date">September 2021</span>)</i></span></div></td></tr></tbody></table> <p>The following titles, all by working physicists, attempt to communicate quantum theory to laypeople, using a minimum of technical apparatus. </p> <ul><li><a href="/wiki/Jim_Al-Khalili" title="Jim Al-Khalili">Jim Al-Khalili</a> (2003). <i>Quantum: A Guide for the Perplexed</i>. Weidenfeld & Nicolson. <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/978-1780225340" title="Special:BookSources/978-1780225340">978-1780225340</a>.</li> <li>Chester, Marvin (1987). <i>Primer of Quantum Mechanics</i>. John Wiley. <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/0486428788" title="Special:BookSources/0486428788">0486428788</a>.</li> <li><a href="/wiki/Brian_Cox_(physicist)" title="Brian Cox (physicist)">Brian Cox</a> and <a href="/wiki/Jeff_Forshaw" title="Jeff Forshaw">Jeff Forshaw</a> (2011) <i><a href="/wiki/The_Quantum_Universe" title="The Quantum Universe">The Quantum Universe</a></i>. Allen Lane. <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/978-1846144325" title="Special:BookSources/978-1846144325">978-1846144325</a>.</li> <li><a href="/wiki/Richard_Feynman" title="Richard Feynman">Richard Feynman</a> (1985). <i><a href="/wiki/QED:_The_Strange_Theory_of_Light_and_Matter" title="QED: The Strange Theory of Light and Matter">QED: The Strange Theory of Light and Matter</a></i>. Princeton University Press. <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/0691083886" title="Special:BookSources/0691083886">0691083886</a>.</li> <li>Ford, Kenneth (2005). <i>The Quantum World</i>. Harvard Univ. Press. Includes elementary particle physics.</li> <li><a href="/wiki/Giancarlo_Ghirardi" title="Giancarlo Ghirardi">Ghirardi, GianCarlo</a> (2004). <i>Sneaking a Look at God's Cards</i>, Gerald Malsbary, trans. Princeton Univ. Press. The most technical of the works cited here. Passages using <a href="/wiki/Algebra" title="Algebra">algebra</a>, <a href="/wiki/Trigonometry" title="Trigonometry">trigonometry</a>, and <a href="/wiki/Bra%E2%80%93ket_notation" title="Bra–ket notation">bra–ket notation</a> can be passed over on a first reading.</li> <li><a href="/wiki/Tony_Hey" title="Tony Hey">Tony Hey</a> and Walters, Patrick (2003). <i>The New Quantum Universe</i>. Cambridge Univ. Press. Includes much about the technologies quantum theory has made possible. <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/978-0521564571" title="Special:BookSources/978-0521564571">978-0521564571</a>.</li> <li>Vladimir G. Ivancevic, Tijana T. Ivancevic (2008). <i>Quantum leap: from Dirac and Feynman, Across the universe, to human body and mind</i>. World Scientific Publishing Company. Provides an intuitive introduction in non-mathematical terms and an introduction in comparatively basic mathematical terms. <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/978-9812819277" title="Special:BookSources/978-9812819277">978-9812819277</a>.</li> <li>J. P. McEvoy and Oscar Zarate (2004). <i>Introducing Quantum Theory</i>. Totem Books. <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/1840465778" title="Special:BookSources/1840465778">1840465778</a>'</li> <li><a href="/wiki/N._David_Mermin" title="N. David Mermin">N. David Mermin</a> (1990). "Spooky actions at a distance: mysteries of the QT" in his <i>Boojums all the way through</i>. Cambridge Univ. Press: 110–76. The author is a rare physicist who tries to communicate to philosophers and humanists. <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/978-0521388801" title="Special:BookSources/978-0521388801">978-0521388801</a>.</li> <li><a href="/wiki/Roland_Omn%C3%A8s" title="Roland Omnès">Roland Omnès</a> (1999). <i>Understanding Quantum Mechanics</i>. Princeton Univ. Press. <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/978-0691004358" title="Special:BookSources/978-0691004358">978-0691004358</a>.</li> <li><a href="/wiki/Victor_Stenger" class="mw-redirect" title="Victor Stenger">Victor Stenger</a> (2000). <i>Timeless Reality: Symmetry, Simplicity, and Multiple Universes</i>. Buffalo NY: Prometheus Books. Chpts. 5–8. <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/978-1573928595" title="Special:BookSources/978-1573928595">978-1573928595</a>.</li> <li><a href="/wiki/Martinus_Veltman" class="mw-redirect" title="Martinus Veltman">Martinus Veltman</a> (2003). <i>Facts and Mysteries in Elementary Particle Physics</i>. World Scientific Publishing Company. <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/978-9812381491" title="Special:BookSources/978-9812381491">978-9812381491</a>.</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=Introduction_to_quantum_mechanics&action=edit&section=27" 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 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/40px-Wikibooks-logo-en-noslogan.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/60px-Wikibooks-logo-en-noslogan.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/80px-Wikibooks-logo-en-noslogan.svg.png 2x" data-file-width="400" data-file-height="400" /></span></span></div> <div class="side-box-text plainlist">The Wikibook <i><a href="https://en.wikibooks.org/wiki/Quantum_Mechanics" class="extiw" title="wikibooks:Quantum Mechanics">Quantum Mechanics</a></i> has a page on the topic of: <i><b><a href="https://en.wikibooks.org/wiki/Quantum_Mechanics/Introduction_to_QM" class="extiw" title="wikibooks:Quantum Mechanics/Introduction to QM">Introduction to Quantum Mechanics</a></b></i></div></div> </div> <ul><li>"<a rel="nofollow" class="external text" href="http://ne.phys.kyushu-u.ac.jp/seminar/MicroWorld1_E/MicroWorld_1_E.html">Microscopic World – Introduction to Quantum Mechanics".</a> by Takada, Kenjiro, emeritus professor at <a href="/wiki/Kyushu_University" title="Kyushu University">Kyushu University</a></li> <li><a rel="nofollow" class="external text" href="https://www.compadre.org/quantum/?">The Quantum Exchange</a> (tutorials and open-source learning software).</li> <li><a rel="nofollow" class="external text" href="https://www.chem1.com/acad/webtext/atoms/">Atoms and the Periodic Table</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20111125050834/http://intro.phys.psu.edu/class/251Labs/10_Interference_%26_Diffraction/Single_and_Double-Slit_Interference.pdf">Single and double slit interference</a></li> <li><a rel="nofollow" class="external text" href="https://demonstrations.wolfram.com/TimeEvolutionOfAWavepacketInASquareWell/">Time-Evolution of a Wavepacket in a Square Well</a> An animated demonstration of a wave packet dispersion over time.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCarroll,_Sean_M." class="citation web cs1"><a href="/wiki/Sean_M._Carroll" title="Sean M. Carroll">Carroll, Sean M.</a> <a rel="nofollow" class="external text" href="http://www.sixtysymbols.com/videos/quantum_mechanics.htm">"Quantum Mechanics (an embarrassment)"</a>. <i>Sixty Symbols</i>. <a href="/wiki/Brady_Haran" title="Brady Haran">Brady Haran</a> for the University of Nottingham.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Sixty+Symbols&rft.atitle=Quantum+Mechanics+%28an+embarrassment%29&rft.au=Carroll%2C+Sean+M.&rft_id=http%3A%2F%2Fwww.sixtysymbols.com%2Fvideos%2Fquantum_mechanics.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntroduction+to+quantum+mechanics" class="Z3988"></span></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Quantum_mechanics" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse 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: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 class="mw-selflink selflink">Introduction</a></li> <li><a href="/wiki/History_of_quantum_mechanics" title="History of quantum mechanics">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 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mechanics</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Types of bonds</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">By symmetry</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/Sigma_bond" title="Sigma bond">Sigma (σ)</a></li> <li><a href="/wiki/Pi_bond" title="Pi bond">Pi (π)</a></li> <li><a href="/wiki/Delta_bond" title="Delta bond">Delta (δ)</a></li> <li><a href="/wiki/Phi_bond" title="Phi bond">Phi (φ)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By <a href="/wiki/Bond_order" title="Bond order">multiplicity</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/Single_bond" title="Single bond">1 (single)</a></li> <li><a href="/wiki/Double_bond" title="Double bond">2 (double)</a></li> <li><a href="/wiki/Triple_bond" title="Triple bond">3 (triple)</a></li> <li><a href="/wiki/Quadruple_bond" title="Quadruple bond">4 (quadruple)</a></li> <li><a href="/wiki/Quintuple_bond" title="Quintuple bond">5 (quintuple)</a></li> <li><a href="/wiki/Sextuple_bond" title="Sextuple bond">6 (sextuple)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By <a href="/wiki/Spin_(physics)" title="Spin (physics)">spin</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/Triplet_state" title="Triplet state">Triplet</a></li> <li><a href="/wiki/Singlet_state" title="Singlet state">Singlet</a></li> <li><a href="/wiki/Exchange_interaction" title="Exchange interaction">Exchange-coupled</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Valence_bond_theory" title="Valence bond theory">Valence bond theory</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</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/Orbital_hybridisation" title="Orbital hybridisation">Hybrid orbital</a></li> <li><a href="/wiki/Resonance_(chemistry)" title="Resonance (chemistry)">Resonance</a></li> <li><a href="/wiki/Lewis_structure" title="Lewis structure">Lewis structure</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Constituent units</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/Covalent_bond" title="Covalent bond">Covalent bond</a></li> <li><a href="/wiki/Lone_pair" title="Lone pair">Lone pair</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Molecular_orbital_theory" title="Molecular orbital theory">Molecular orbital theory</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</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/Molecular_orbital" title="Molecular orbital">Molecular orbital</a></li> <li><a href="/wiki/Linear_combination_of_atomic_orbitals" title="Linear combination of atomic orbitals">LCAO</a></li> <li><a href="/wiki/Molecular_orbital_diagram" title="Molecular orbital diagram">MO diagram</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Constituent units</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/Bonding_molecular_orbital" title="Bonding molecular orbital">Bonding MO</a></li> <li><a href="/wiki/Non-bonding_orbital" title="Non-bonding orbital">Non-bonding MO</a></li> <li><a href="/wiki/Antibonding_molecular_orbital" title="Antibonding molecular orbital">Antibonding MO</a></li></ul> </div></td></tr></tbody></table><div></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" 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style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Principal_quantum_number" title="Principal quantum number">Principal quantum number (<span class="texhtml mvar" style="font-style:italic;">n</span>)</a></li> <li><a href="/wiki/Azimuthal_quantum_number" title="Azimuthal quantum number">Azimuthal quantum number (<span class="texhtml mvar" style="font-style:italic;">ℓ</span>)</a></li> <li><a href="/wiki/Magnetic_quantum_number" title="Magnetic quantum number">Magnetic quantum number (<span class="texhtml mvar" style="font-style:italic;">m</span>)</a></li> <li><a href="/wiki/Spin_quantum_number" title="Spin quantum number">Spin quantum number (<span class="texhtml mvar" style="font-style:italic;">s</span>)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Ground-state configurations</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 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