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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%A1%E0%A7%87%E0%A6%AD%E0%A6%BF%E0%A6%B8%E0%A6%A8-%E0%A6%9C%E0%A6%BE%E0%A6%B0%E0%A7%8D%E0%A6%AE%E0%A6%BE%E0%A6%B0_%E0%A6%AA%E0%A6%B0%E0%A7%80%E0%A6%95%E0%A7%8D%E0%A6%B7%E0%A6%A3" title="ডেভিসন-জার্মার পরীক্ষণ – Bangla" lang="bn" hreflang="bn" data-title="ডেভিসন-জার্মার পরীক্ষণ" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://ca.wikipedia.org/wiki/Experiment_de_Davisson-Germer" title="Experiment de Davisson-Germer – Catalan" lang="ca" hreflang="ca" data-title="Experiment de Davisson-Germer" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Davisson%C5%AFv%E2%80%93Germer%C5%AFv_experiment" title="Davissonův–Germerův experiment – Czech" lang="cs" hreflang="cs" data-title="Davissonův–Germerův experiment" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Davisson-Germer-Experiment" title="Davisson-Germer-Experiment – German" lang="de" hreflang="de" data-title="Davisson-Germer-Experiment" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Experimento_de_Davisson-Germer" title="Experimento de Davisson-Germer – Spanish" lang="es" hreflang="es" data-title="Experimento de Davisson-Germer" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A2%D8%B2%D9%85%D8%A7%DB%8C%D8%B4_%D8%AF%DB%8C%D9%88%DB%8C%D8%B3%D9%88%D9%86_%DA%AF%D8%B1%D9%85%D8%B1" title="آزمایش دیویسون گرمر – Persian" lang="fa" hreflang="fa" data-title="آزمایش دیویسون گرمر" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Exp%C3%A9rience_de_Davisson-Germer" title="Expérience de Davisson-Germer – French" lang="fr" hreflang="fr" data-title="Expérience de Davisson-Germer" 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/%EB%8D%B0%EC%9D%B4%EB%B9%84%EC%8A%A8-%EA%B1%B0%EB%A8%B8_%EC%8B%A4%ED%97%98" title="데이비슨-거머 실험 – Korean" lang="ko" hreflang="ko" data-title="데이비슨-거머 실험" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B4%D5%A5%D5%B5%D5%BE%D5%AB%D5%BD%D5%B8%D5%B6-%D5%8B%D5%A5%D6%80%D5%B4%D5%A5%D6%80%D5%AB_%D6%83%D5%B8%D6%80%D5%B1" title="Դեյվիսոն-Ջերմերի փորձ – Armenian" lang="hy" hreflang="hy" data-title="Դեյվիսոն-Ջերմերի փորձ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Esperimento_di_Davisson_e_Germer" title="Esperimento di Davisson e Germer – Italian" lang="it" hreflang="it" data-title="Esperimento di Davisson e Germer" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Davisson%E2%80%93Germer-k%C3%ADs%C3%A9rlet" title="Davisson–Germer-kísérlet – Hungarian" lang="hu" hreflang="hu" data-title="Davisson–Germer-kísérlet" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%A1%E0%B5%87%E0%B4%B5%E0%B4%BF%E0%B4%B8%E0%B5%BA-%E0%B4%9C%E0%B5%86%E0%B5%BC%E0%B4%AE%E0%B5%BC_%E0%B4%AA%E0%B4%B0%E0%B5%80%E0%B4%95%E0%B5%8D%E0%B4%B7%E0%B4%A3%E0%B4%82" title="ഡേവിസൺ-ജെർമർ പരീക്ഷണം – Malayalam" lang="ml" hreflang="ml" data-title="ഡേവിസൺ-ജെർമർ പരീക്ഷണം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%87%E3%82%A4%E3%83%B4%E3%82%A3%E3%82%BD%E3%83%B3%EF%BC%9D%E3%82%AC%E3%83%BC%E3%83%9E%E3%83%BC%E3%81%AE%E5%AE%9F%E9%A8%93" title="デイヴィソン＝ガーマーの実験 – Japanese" lang="ja" hreflang="ja" data-title="デイヴィソン＝ガーマーの実験" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Devisson-Germer_tajribasi" title="Devisson-Germer tajribasi – Uzbek" lang="uz" hreflang="uz" data-title="Devisson-Germer tajribasi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Do%C5%9Bwiadczenie_Davissona_i_Germera" title="Doświadczenie Davissona i Germera – Polish" lang="pl" hreflang="pl" data-title="Doświadczenie Davissona i Germera" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Experimento_de_Davisson%E2%80%93Germer" title="Experimento de Davisson–Germer – Portuguese" lang="pt" hreflang="pt" data-title="Experimento de Davisson–Germer" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://ru.wikipedia.org/wiki/%D0%9E%D0%BF%D1%8B%D1%82_%D0%94%D1%8D%D0%B2%D0%B8%D1%81%D1%81%D0%BE%D0%BD%D0%B0_%E2%80%94_%D0%94%D0%B6%D0%B5%D1%80%D0%BC%D0%B5%D1%80%D0%B0" title="Опыт Дэвиссона — Джермера – Russian" lang="ru" hreflang="ru" data-title="Опыт Дэвиссона — Джермера" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Davissonov_Germerov_experiment" title="Davissonov Germerov experiment – Slovak" lang="sk" hreflang="sk" data-title="Davissonov Germerov experiment" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%9F%E0%AF%87%E0%AE%B5%E0%AE%BF%E0%AE%9A%E0%AE%A9%E0%AF%8D-%E0%AE%9A%E0%AF%86%E0%AE%B0%E0%AF%8D%E0%AE%AE%E0%AE%B0%E0%AF%8D_%E0%AE%9A%E0%AF%8B%E0%AE%A4%E0%AE%A9%E0%AF%88" title="டேவிசன்-செர்மர் சோதனை – Tamil" lang="ta" hreflang="ta" data-title="டேவிசன்-செர்மர் சோதனை" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Davisson-Germer_deneyi" title="Davisson-Germer deneyi – Turkish" lang="tr" hreflang="tr" data-title="Davisson-Germer deneyi" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a 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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 href="/wiki/Introduction_to_quantum_mechanics" title="Introduction to quantum mechanics">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"><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 class="mw-selflink selflink">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> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Davisson_and_Germer.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Davisson_and_Germer.jpg/220px-Davisson_and_Germer.jpg" decoding="async" width="220" height="223" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Davisson_and_Germer.jpg/330px-Davisson_and_Germer.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/9/99/Davisson_and_Germer.jpg 2x" data-file-width="334" data-file-height="339" /></a><figcaption>Davisson and Germer in 1927</figcaption></figure> <p>The <b>Davisson–Germer experiment</b> was a 1923–1927 experiment by <a href="/wiki/Clinton_Davisson" title="Clinton Davisson">Clinton Davisson</a> and <a href="/wiki/Lester_Germer" title="Lester Germer">Lester Germer</a> at <a href="/wiki/Bell_Labs" title="Bell Labs">Western Electric (later Bell Labs)</a>,<sup id="cite_ref-:0_1-0" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:1_2-0" class="reference"><a href="#cite_note-:1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-ncbi.nlm.nih.gov_3-0" class="reference"><a href="#cite_note-ncbi.nlm.nih.gov-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> in which electrons, scattered by the surface of a crystal of nickel metal, displayed a diffraction pattern. This confirmed the <a href="/wiki/Matter_wave" title="Matter wave">hypothesis</a>, advanced by <a href="/wiki/Louis_de_Broglie" title="Louis de Broglie">Louis de Broglie</a> in 1924, of wave-particle duality, and also the wave mechanics approach of the <a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger equation</a>. It was an experimental milestone in the creation of <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History_and_overview">History and overview</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Davisson%E2%80%93Germer_experiment&action=edit&section=1" title="Edit section: History and overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>According to <a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell's equations</a> in the late 19th century, light was thought to consist of waves of electromagnetic fields and matter was thought to consist of localized particles. However, this was challenged in <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a>'s 1905 paper on the <a href="/wiki/Photoelectric_effect" title="Photoelectric effect">photoelectric effect</a>, which described light as discrete and localized quanta of energy (now called <a href="/wiki/Photon" title="Photon">photons</a>), which won him the <a href="/wiki/Nobel_Prize_in_Physics" title="Nobel Prize in Physics">Nobel Prize in Physics</a> in 1921. In 1924 <a href="/wiki/Louis_de_Broglie" title="Louis de Broglie">Louis de Broglie</a> presented his thesis concerning the wave–particle duality theory, which proposed the idea that all matter displays the wave–particle duality of photons.<sup id="cite_ref-EisbergResnick_4-0" class="reference"><a href="#cite_note-EisbergResnick-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> According to de Broglie, for all matter and for radiation alike, the energy <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> of the particle was related to the frequency of its associated wave <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 \nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }"></span> by the <a href="/wiki/Planck_constant#Origins" title="Planck constant">Planck relation</a>: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=h\nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>h</mi> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=h\nu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c6c0386dc6d9530519404f95570fcc8548ed2326" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.445ex; height:2.176ex;" alt="{\displaystyle E=h\nu }"></span> And that the momentum of the particle <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> was related to its wavelength by what is now known as the <a href="/wiki/De_Broglie_relation" class="mw-redirect" title="De Broglie relation">de Broglie relation</a>: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda ={\frac {h}{p}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>h</mi> <mi>p</mi> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda ={\frac {h}{p}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ea61dba4f570d474341b6f5ff22b0f26f52c1a87" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:7.276ex; height:5.843ex;" alt="{\displaystyle \lambda ={\frac {h}{p}},}"></span> where <span class="texhtml"><i>h</i></span> is the <a href="/wiki/Planck_constant" title="Planck constant">Planck constant</a>. </p><p>An important contribution to the Davisson–Germer experiment was made by <a href="/wiki/Walter_M._Elsasser" title="Walter M. Elsasser">Walter M. Elsasser</a> in Göttingen in the 1920s, who remarked that the wave-like nature of matter might be investigated by <a href="/wiki/Electron_scattering_experiment" class="mw-redirect" title="Electron scattering experiment">electron scattering experiments</a> on crystalline solids, just as the wave-like nature of X-rays had been confirmed through <a href="/wiki/Barkla" class="mw-redirect" title="Barkla">Barkla</a>'s X-ray scattering experiments on <a href="/wiki/Crystal" title="Crystal">crystalline solids</a>.<sup id="cite_ref-EisbergResnick_4-1" class="reference"><a href="#cite_note-EisbergResnick-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>This suggestion of Elsasser was then communicated by his senior colleague (and later Nobel Prize recipient) <a href="/wiki/Max_Born" title="Max Born">Max Born</a> to physicists in England. When the Davisson and Germer experiment was performed, the results of the experiment were explained by Elsasser's proposition. However the initial intention of the Davisson and Germer experiment was not to confirm the <a href="/wiki/Matter_wave" title="Matter wave">de Broglie hypothesis</a>, but rather to study the surface of nickel. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Bell_Labs_APS_plaque_west_side_of_Westbeth_door_jeh_edited.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Bell_Labs_APS_plaque_west_side_of_Westbeth_door_jeh_edited.jpg/220px-Bell_Labs_APS_plaque_west_side_of_Westbeth_door_jeh_edited.jpg" decoding="async" width="220" height="118" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Bell_Labs_APS_plaque_west_side_of_Westbeth_door_jeh_edited.jpg/330px-Bell_Labs_APS_plaque_west_side_of_Westbeth_door_jeh_edited.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Bell_Labs_APS_plaque_west_side_of_Westbeth_door_jeh_edited.jpg/440px-Bell_Labs_APS_plaque_west_side_of_Westbeth_door_jeh_edited.jpg 2x" data-file-width="3460" data-file-height="1853" /></a><figcaption>American Physical Society plaque in Manhattan commemorates the experiment</figcaption></figure> <p>In 1927 at <a href="/wiki/Bell_Labs" title="Bell Labs">Bell Labs</a>, Clinton Davisson and Lester Germer fired slow moving electrons at a crystalline nickel target. The angular dependence of the reflected electron intensity was measured<sup id="cite_ref-:0_1-1" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:1_2-1" class="reference"><a href="#cite_note-:1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> and was determined to have a similar diffraction pattern as those predicted by Bragg for X-rays; some small, but significant differences<sup id="cite_ref-ncbi.nlm.nih.gov_3-1" class="reference"><a href="#cite_note-ncbi.nlm.nih.gov-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> were due to the average potential which <a href="/wiki/Hans_Bethe" title="Hans Bethe">Hans Bethe</a> showed in his more complete analysis.<sup id="cite_ref-:2_6-0" class="reference"><a href="#cite_note-:2-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> At the same time <a href="/wiki/George_Paget_Thomson" title="George Paget Thomson">George Paget Thomson</a> and his student Alexander Reid independently demonstrated the same effect firing electrons through celluloid films to produce a diffraction pattern, and Davisson and Thomson shared the Nobel Prize in Physics in 1937.<sup id="cite_ref-EisbergResnick_4-2" class="reference"><a href="#cite_note-EisbergResnick-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><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> The exclusion of Germer from sharing the prize has puzzled physicists ever since.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> The Davisson–Germer experiment confirmed the de Broglie hypothesis that matter has wave-like behavior. This, in combination with the <a href="/wiki/Compton_effect" class="mw-redirect" title="Compton effect">Compton effect</a> discovered by <a href="/wiki/Arthur_Compton" title="Arthur Compton">Arthur Compton</a> (who won the Nobel Prize for Physics in 1927),<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> established the wave–particle duality hypothesis which was a fundamental step in quantum theory. </p> <div class="mw-heading mw-heading2"><h2 id="Early_experiments">Early experiments</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Davisson%E2%80%93Germer_experiment&action=edit&section=2" title="Edit section: Early experiments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Davisson began work in 1921 to study electron bombardment and secondary electron emissions. A series of experiments continued through 1925. </p><p>Prior to 1923, Davisson had been working with Charles H. Kunsman on detecting the effects of electron bombardment on tungsten when they noticed that 1% of the electrons bounced straight back to the electron gun in elastic scattering. This small but unexpected result led Davisson to theorize that he could examine the electron configuration of the atom in an analogous manner to how the <a href="/wiki/Gold_foil_experiment" class="mw-redirect" title="Gold foil experiment">Rutherford alpha particle scattering</a> had examined the nucleus. They changed to a high vacuum and used nickel along with various other metals with unimpressive results.<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> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Davisson-Germer_experiment.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Davisson-Germer_experiment.svg/220px-Davisson-Germer_experiment.svg.png" decoding="async" width="220" height="159" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Davisson-Germer_experiment.svg/330px-Davisson-Germer_experiment.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Davisson-Germer_experiment.svg/440px-Davisson-Germer_experiment.svg.png 2x" data-file-width="900" data-file-height="650" /></a><figcaption>Experimental setup</figcaption></figure> <p>In October 1924 when Germer joined the experiment, Davisson’s actual objective was to study the surface of a piece of nickel by directing a beam of electrons at the surface and observing how many electrons bounced off at various angles. They expected that because of the small size of electrons, even the smoothest crystal surface would be too rough and thus the electron beam would experience diffused reflection.<sup id="cite_ref-Hugh_D._Young_2004_11-0" class="reference"><a href="#cite_note-Hugh_D._Young_2004-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>The experiment consisted of firing an electron beam (from an <a href="/wiki/Electron_gun" title="Electron gun">electron gun</a>, an <a href="/wiki/Electrostatic_particle_accelerator" title="Electrostatic particle accelerator">electrostatic particle accelerator</a>) at a nickel crystal, perpendicular to the surface of the crystal, and measuring how the number of reflected electrons varied as the angle between the detector and the nickel surface varied. The electron gun was a heated tungsten filament that released thermally excited electrons which were then accelerated through an electric potential difference, giving them a certain amount of kinetic energy, towards the nickel crystal. To avoid collisions of the electrons with other atoms on their way towards the surface, the experiment was conducted in a vacuum chamber. To measure the number of electrons that were scattered at different angles, a <a href="/wiki/Faraday_cup" title="Faraday cup">faraday cup</a> electron detector that could be moved on an arc path about the crystal was used. The detector was designed to accept only <a href="/wiki/Elastic_scattering" title="Elastic scattering">elastically scattered electrons</a>. </p><p>During the experiment, air accidentally entered the chamber, producing an oxide film on the nickel surface. To remove the oxide, Davisson and Germer heated the specimen in a high temperature oven, not knowing that this caused the formerly polycrystalline structure of the nickel to form large single crystal areas with crystal planes continuous over the width of the electron beam.<sup id="cite_ref-Hugh_D._Young_2004_11-1" class="reference"><a href="#cite_note-Hugh_D._Young_2004-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>When they started the experiment again and the electrons hit the surface, they were scattered by nickel atoms in crystal planes (so the atoms were regularly spaced) of the crystal. This, in 1925, generated a diffraction pattern with unexpected and uncorrelated peaks due to the heating causing a ten crystal faceted area. They changed the experiment to a single crystal and started again. </p> <div class="mw-heading mw-heading2"><h2 id="Breakthrough">Breakthrough</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Davisson%E2%80%93Germer_experiment&action=edit&section=3" title="Edit section: Breakthrough"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>On his second honeymoon, Davisson attended the Oxford meeting of the British Association for the Advancement of Science in summer 1926. At this meeting, he learned of the recent advances in quantum mechanics. To Davisson's surprise, <a href="/wiki/Max_Born" title="Max Born">Max Born</a> gave a lecture that used the uncorrelated diffraction curves from Davisson's 1923 research on platinum with Kunsman,<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> using the data as confirmation of the de Broglie hypothesis of which Davisson was unaware.<sup id="cite_ref-Gehrenbeck_1978_34–41_13-0" class="reference"><a href="#cite_note-Gehrenbeck_1978_34–41-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>Davisson then learned that in prior years, other scientists – Walter Elsasser, E. G. Dymond, and Blackett, James Chadwick, and Charles Ellis – had attempted similar diffraction experiments, but were unable to generate low enough vacuums or detect the low-intensity beams needed.<sup id="cite_ref-Gehrenbeck_1978_34–41_13-1" class="reference"><a href="#cite_note-Gehrenbeck_1978_34–41-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>Returning to the United States, Davisson made modifications to the tube design and detector mounting, adding azimuth in addition to colatitude. Following experiments generated a strong signal peak at 65 V and an angle <span class="nowrap"><i>θ</i> = 45°</span>. He published a note to <i>Nature</i> titled, "The Scattering of Electrons by a Single Crystal of Nickel".<sup id="cite_ref-:0_1-2" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:The_Scattering_of_Electrons_by_a_Single_Crystal_of_Nickel_Fig._2.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/The_Scattering_of_Electrons_by_a_Single_Crystal_of_Nickel_Fig._2.jpg/220px-The_Scattering_of_Electrons_by_a_Single_Crystal_of_Nickel_Fig._2.jpg" decoding="async" width="220" height="209" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/The_Scattering_of_Electrons_by_a_Single_Crystal_of_Nickel_Fig._2.jpg/330px-The_Scattering_of_Electrons_by_a_Single_Crystal_of_Nickel_Fig._2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a2/The_Scattering_of_Electrons_by_a_Single_Crystal_of_Nickel_Fig._2.jpg/440px-The_Scattering_of_Electrons_by_a_Single_Crystal_of_Nickel_Fig._2.jpg 2x" data-file-width="1602" data-file-height="1521" /></a><figcaption>Graph of the electrical current vs electron beam azimuth angle from the 1927 "The Scattering of Electrons by a Single Crystal of Nickel" paper<sup id="cite_ref-:0_1-3" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>. The presence of peaks and troughs is consistent with a diffraction pattern and suggests a wave-like nature of electrons.</figcaption></figure> <p>Questions still needed to be answered and experimentation continued through 1927, because Davisson was now familiar with the de Broglie formula and had designed the test to see if any effect could be discerned for a changed electron wavelength <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b43d0ea3c9c025af1be9128e62a18fa74bedda2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }"></span>, according to the de Broglie relationship, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda =h/(2mE)^{1/2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mo>=</mo> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mi>m</mi> <mi>E</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda =h/(2mE)^{1/2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ceb14c0e37cbe6bd5fb4a31f2b8f47ad35c56682" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.441ex; height:3.343ex;" alt="{\displaystyle \lambda =h/(2mE)^{1/2}}"></span> which they knew should create a peak at 78 and not 65 V as their paper had shown. Because of their failure to correlate with the de Broglie formula, their paper introduced an ad hoc contraction factor of 0.7, which, however, could only explain eight of the thirteen beams.<sup id="cite_ref-Gehrenbeck_1978_34–41_13-2" class="reference"><a href="#cite_note-Gehrenbeck_1978_34–41-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><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><p>By varying the applied voltage to the electron gun, the maximum intensity of electrons diffracted by the atomic surface was found at different angles. The highest intensity was observed at an angle <span class="nowrap"><i>θ</i> = 50°</span> with a voltage of 54 V, giving the electrons a kinetic energy of <span class="nowrap"><span data-sort-value="6982865175302980000♠"></span>54 <a href="/wiki/Electronvolt" title="Electronvolt">eV</a></span>.<sup id="cite_ref-EisbergResnick_4-3" class="reference"><a href="#cite_note-EisbergResnick-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>As <a href="/wiki/Max_von_Laue" title="Max von Laue">Max von Laue</a> proved in 1912, the periodic crystal structure serves as a type of three-dimensional diffraction grating. The angles of maximum reflection are given by Bragg's condition for constructive interference from an array, <a href="/wiki/Bragg%27s_law" title="Bragg's law">Bragg's law</a> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n\lambda =2d\sin \left(90^{\circ }-{\frac {\theta }{2}}\right),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mi>λ</mi> <mo>=</mo> <mn>2</mn> <mi>d</mi> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <msup> <mn>90</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>θ</mi> <mn>2</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n\lambda =2d\sin \left(90^{\circ }-{\frac {\theta }{2}}\right),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98daf6d836b37f2569384ca10d1669b7f173b6bc" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:23.756ex; height:6.176ex;" alt="{\displaystyle n\lambda =2d\sin \left(90^{\circ }-{\frac {\theta }{2}}\right),}"></span> for <span class="texhtml"><i>n</i> = 1</span>, <span class="texhtml"><i>θ</i> = 50°</span>, and for the spacing of the <a href="/wiki/Crystal_lattice" class="mw-redirect" title="Crystal lattice">crystalline planes</a> of nickel (<span class="texhtml"><i>d</i> = 0.091 nm</span>) obtained from previous <a href="/wiki/X-ray_scattering" class="mw-redirect" title="X-ray scattering">X-ray scattering</a> experiments on crystalline nickel.<sup id="cite_ref-EisbergResnick_4-4" class="reference"><a href="#cite_note-EisbergResnick-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>According to the de Broglie relation, electrons with kinetic energy of <span class="nowrap"><span data-sort-value="6982865175302980000♠"></span>54 <a href="/wiki/Electronvolt" title="Electronvolt">eV</a></span> have a wavelength of <span class="nowrap"><span data-sort-value="6990167000000000000♠"></span>0.167 <a href="/wiki/Nanometre" title="Nanometre">nm</a></span>. The experimental outcome was <span class="nowrap"><span data-sort-value="6990165000000000000♠"></span>0.165 nm</span> via <a href="/wiki/Bragg%27s_law" title="Bragg's law">Bragg's law</a>, which closely matched the predictions. As Davisson and Germer state in their 1928 follow-up paper to their Nobel prize winning paper, "These results, including the failure of the data to satisfy the Bragg formula, are in accord with those previously obtained in our experiments on electron diffraction. The reflection data fail to satisfy the Bragg relation for the same reason that the electron diffraction beams fail to coincide with their Laue beam analogues."<sup id="cite_ref-ncbi.nlm.nih.gov_3-2" class="reference"><a href="#cite_note-ncbi.nlm.nih.gov-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> However, they add, "The calculated wave-lengths are in excellent agreement with the theoretical values of h/mv as shown in the accompanying table."<sup id="cite_ref-ncbi.nlm.nih.gov_3-3" class="reference"><a href="#cite_note-ncbi.nlm.nih.gov-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> So although electron energy diffraction does not follow the Bragg law, it did confirm de Broglie's theory that particles behave like waves. The full explanation was provided by <a href="/wiki/Hans_Bethe" title="Hans Bethe">Hans Bethe</a> who solved <a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger equation</a><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> for the case of electron diffraction.<sup id="cite_ref-:2_6-1" class="reference"><a href="#cite_note-:2-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>Davisson and Germer's accidental discovery of the diffraction of electrons was the first direct evidence confirming de Broglie's hypothesis that particles can have wave properties as well. </p><p>Davisson's attention to detail, his resources for conducting basic research, the expertise of colleagues, and luck all contributed to the experimental success. </p> <div class="mw-heading mw-heading2"><h2 id="Practical_applications">Practical applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Davisson%E2%80%93Germer_experiment&action=edit&section=4" title="Edit section: Practical applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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">Main article: <a href="/wiki/Electron_diffraction" title="Electron diffraction">Electron diffraction</a></div> <p>The specific approach used by Davisson and Germer used low energy electrons, what is now called <a href="/wiki/Low-energy_electron_diffraction" title="Low-energy electron diffraction">low-energy electron diffraction</a> (LEED). It wasn't until much later that development of experimental methods exploiting <a href="/wiki/Ultra-high_vacuum" title="Ultra-high vacuum">ultra-high vacuum</a> technologies (e.g. the approach described by Alpert in 1953<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>) enabled the extensive use of <a href="/wiki/Low-energy_electron_diffraction" title="Low-energy electron diffraction">LEED diffraction</a> to explore the surfaces of crystallized elements and the spacing between atoms.<sup id="cite_ref-VanHove_17-0" class="reference"><a href="#cite_note-VanHove-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> Methods where higher energy electrons are used for <a href="/wiki/Electron_diffraction" title="Electron diffraction">diffraction</a> in many different ways developed much earlier. </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=Davisson%E2%80%93Germer_experiment&action=edit&section=5" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width reflist-columns-2"> <ol class="references"> <li id="cite_note-:0-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:0_1-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:0_1-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFDavissonGermer1927" class="citation journal cs1">Davisson, C.; Germer, L. H. (1927). <a class="external text" href="https://commons.wikimedia.org/w/index.php?title=File%3AThe_Scattering_of_Electrons_by_a_Single_Crystal_of_Nickel.pdf&page=1">"The Scattering of Electrons by a Single Crystal of Nickel"</a>. <i>Nature</i>. <b>119</b> (2998): 558. <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/1927Natur.119..558D">1927Natur.119..558D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F119558a0">10.1038/119558a0</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:4104602">4104602</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=The+Scattering+of+Electrons+by+a+Single+Crystal+of+Nickel&rft.volume=119&rft.issue=2998&rft.pages=558&rft.date=1927&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4104602%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1038%2F119558a0&rft_id=info%3Abibcode%2F1927Natur.119..558D&rft.aulast=Davisson&rft.aufirst=C.&rft.au=Germer%2C+L.+H.&rft_id=https%3A%2F%2Fcommons.wikimedia.org%2Fw%2Findex.php%3Ftitle%3DFile%253AThe_Scattering_of_Electrons_by_a_Single_Crystal_of_Nickel.pdf%26page%3D1&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADavisson%E2%80%93Germer+experiment" class="Z3988"></span></span> </li> <li id="cite_note-:1-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDavissonGermer1927" class="citation journal cs1">Davisson, C.; Germer, L. H. (1927). <a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRev.30.705">"Diffraction of Electrons by a Crystal of Nickel"</a>. <i>Physical Review</i>. <b>30</b> (6): <span class="nowrap">705–</span>740. <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/1927PhRv...30..705D">1927PhRv...30..705D</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.30.705">10.1103/PhysRev.30.705</a></span>. <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=Diffraction+of+Electrons+by+a+Crystal+of+Nickel&rft.volume=30&rft.issue=6&rft.pages=%3Cspan+class%3D%22nowrap%22%3E705-%3C%2Fspan%3E740&rft.date=1927&rft.issn=0031-899X&rft_id=info%3Adoi%2F10.1103%2FPhysRev.30.705&rft_id=info%3Abibcode%2F1927PhRv...30..705D&rft.aulast=Davisson&rft.aufirst=C.&rft.au=Germer%2C+L.+H.&rft_id=https%3A%2F%2Fdoi.org%2F10.1103%252FPhysRev.30.705&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADavisson%E2%80%93Germer+experiment" class="Z3988"></span></span> </li> <li id="cite_note-ncbi.nlm.nih.gov-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-ncbi.nlm.nih.gov_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-ncbi.nlm.nih.gov_3-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-ncbi.nlm.nih.gov_3-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-ncbi.nlm.nih.gov_3-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDavissonGermer1928" class="citation journal cs1">Davisson, C. J.; Germer, L. H. (1928). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1085484">"Reflection of Electrons by a Crystal of Nickel"</a>. <i>Proceedings of the National Academy of Sciences of the United States of America</i>. <b>14</b> (4): <span class="nowrap">317–</span>322. <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/1928PNAS...14..317D">1928PNAS...14..317D</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/10.1073%2Fpnas.14.4.317">10.1073/pnas.14.4.317</a></span>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1085484">1085484</a></span>. <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/16587341">16587341</a>.</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+National+Academy+of+Sciences+of+the+United+States+of+America&rft.atitle=Reflection+of+Electrons+by+a+Crystal+of+Nickel&rft.volume=14&rft.issue=4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E317-%3C%2Fspan%3E322&rft.date=1928&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC1085484%23id-name%3DPMC&rft_id=info%3Apmid%2F16587341&rft_id=info%3Adoi%2F10.1073%2Fpnas.14.4.317&rft_id=info%3Abibcode%2F1928PNAS...14..317D&rft.aulast=Davisson&rft.aufirst=C.+J.&rft.au=Germer%2C+L.+H.&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC1085484&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADavisson%E2%80%93Germer+experiment" class="Z3988"></span></span> </li> <li id="cite_note-EisbergResnick-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-EisbergResnick_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-EisbergResnick_4-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-EisbergResnick_4-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-EisbergResnick_4-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-EisbergResnick_4-4"><sup><i><b>e</b></i></sup></a></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEisberg,_R.Resnick,_R.1985" class="citation book cs1">Eisberg, R.; Resnick, R. (1985). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/quantumphysicsof00eisb">"Chapter 3 – de Broglie's Postulate—Wavelike Properties of Particles"</a></span>. <i>Quantum Physics: of Atoms, Molecules, Solids, Nuclei, and Particles</i> (2nd ed.). <a href="/wiki/John_Wiley_%26_Sons" class="mw-redirect" title="John Wiley & Sons">John Wiley & Sons</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-87373-0" title="Special:BookSources/978-0-471-87373-0"><bdi>978-0-471-87373-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Chapter+3+%E2%80%93+de+Broglie%27s+Postulate%E2%80%94Wavelike+Properties+of+Particles&rft.btitle=Quantum+Physics%3A+of+Atoms%2C+Molecules%2C+Solids%2C+Nuclei%2C+and+Particles&rft.edition=2nd&rft.pub=John+Wiley+%26+Sons&rft.date=1985&rft.isbn=978-0-471-87373-0&rft.au=Eisberg%2C+R.&rft.au=Resnick%2C+R.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fquantumphysicsof00eisb&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADavisson%E2%80%93Germer+experiment" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRubin,_H.1995" class="citation book cs1">Rubin, H. 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(1928). <a rel="nofollow" class="external text" href="https://onlinelibrary.wiley.com/doi/10.1002/andp.19283921704">"Theorie der Beugung von Elektronen an Kristallen"</a>. <i>Annalen der Physik</i> (in German). <b>392</b> (17): <span class="nowrap">55–</span>129. <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/1928AnP...392...55B">1928AnP...392...55B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.19283921704">10.1002/andp.19283921704</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annalen+der+Physik&rft.atitle=Theorie+der+Beugung+von+Elektronen+an+Kristallen&rft.volume=392&rft.issue=17&rft.pages=%3Cspan+class%3D%22nowrap%22%3E55-%3C%2Fspan%3E129&rft.date=1928&rft_id=info%3Adoi%2F10.1002%2Fandp.19283921704&rft_id=info%3Abibcode%2F1928AnP...392...55B&rft.aulast=Bethe&rft.aufirst=H.&rft_id=https%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1002%2Fandp.19283921704&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADavisson%E2%80%93Germer+experiment" 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="CITEREFDavisson,_Clinton_JosephThomson,_George_Paget1937" class="citation web cs1">Davisson, Clinton Joseph; Thomson, George Paget (1937). <a rel="nofollow" class="external text" href="https://www.nobelprize.org/nobel_prizes/physics/laureates/1937/">"Clinton Joseph Davisson and George Paget Thomson for their experimental discovery of the diffraction of electrons by crystals"</a>. The Nobel Foundation.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Clinton+Joseph+Davisson+and+George+Paget+Thomson+for+their+experimental+discovery+of+the+diffraction+of+electrons+by+crystals&rft.pub=The+Nobel+Foundation&rft.date=1937&rft.au=Davisson%2C+Clinton+Joseph&rft.au=Thomson%2C+George+Paget&rft_id=https%3A%2F%2Fwww.nobelprize.org%2Fnobel_prizes%2Fphysics%2Flaureates%2F1937%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADavisson%E2%80%93Germer+experiment" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSmart2016" class="citation journal cs1">Smart, Ashley G. 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H. (1921). <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/1645064">"The Scattering of Electrons by Nickel"</a>. <i>Science</i>. <b>54</b> (1404): 523. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fscience.54.1404.522">10.1126/science.54.1404.522</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/0036-8075">0036-8075</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Science&rft.atitle=The+Scattering+of+Electrons+by+Nickel&rft.volume=54&rft.issue=1404&rft.pages=523&rft.date=1921&rft_id=info%3Adoi%2F10.1126%2Fscience.54.1404.522&rft.issn=0036-8075&rft.aulast=Davisson&rft.aufirst=C.&rft.au=Kunsman%2C+C.+H.&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F1645064&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADavisson%E2%80%93Germer+experiment" class="Z3988"></span></span> </li> <li id="cite_note-Hugh_D._Young_2004-11"><span class="mw-cite-backlink">^ <a href="#cite_ref-Hugh_D._Young_2004_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Hugh_D._Young_2004_11-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Young, Hugh D. and Freedman, Roger A. 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(1978). <a rel="nofollow" class="external text" href="http://www.if.ufrj.br/~tclp/estadosolido/phystoday34(78).pdf">"Electron diffraction: fifty years ago"</a> <span class="cs1-format">(PDF)</span>. <i>Physics Today</i>. <b>31</b> (1): <span class="nowrap">34–</span>41. <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/1978PhT....31a..34G">1978PhT....31a..34G</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%2F1.3001830">10.1063/1.3001830</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=Electron+diffraction%3A+fifty+years+ago&rft.volume=31&rft.issue=1&rft.pages=%3Cspan+class%3D%22nowrap%22%3E34-%3C%2Fspan%3E41&rft.date=1978&rft_id=info%3Adoi%2F10.1063%2F1.3001830&rft_id=info%3Abibcode%2F1978PhT....31a..34G&rft.aulast=Gehrenbeck&rft.aufirst=Richard+K.&rft_id=http%3A%2F%2Fwww.if.ufrj.br%2F~tclp%2Festadosolido%2Fphystoday34%2878%29.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADavisson%E2%80%93Germer+experiment" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFC._DavissonL._H._Germer1927" class="citation web cs1">C. 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Retrieved <span class="nowrap">13 December</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Diffraction+of+Electrons+by+a+Crystal+of+Nickel&rft.date=1927-12&rft.au=C.+Davisson&rft.au=L.+H.+Germer&rft_id=http%3A%2F%2Fhermes.ffn.ub.es%2Fluisnavarro%2Fnuevo_maletin%2FDavisson_Germer_1927.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADavisson%E2%80%93Germer+experiment" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchrödinger1926" class="citation journal cs1">Schrödinger, E. (1926). <a rel="nofollow" class="external text" href="https://link.aps.org/doi/10.1103/PhysRev.28.1049">"An Undulatory Theory of the Mechanics of Atoms and Molecules"</a>. <i>Physical Review</i>. <b>28</b> (6): <span class="nowrap">1049–</span>1070. <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/1926PhRv...28.1049S">1926PhRv...28.1049S</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.28.1049">10.1103/PhysRev.28.1049</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=An+Undulatory+Theory+of+the+Mechanics+of+Atoms+and+Molecules&rft.volume=28&rft.issue=6&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1049-%3C%2Fspan%3E1070&rft.date=1926&rft_id=info%3Adoi%2F10.1103%2FPhysRev.28.1049&rft_id=info%3Abibcode%2F1926PhRv...28.1049S&rft.aulast=Schr%C3%B6dinger&rft.aufirst=E.&rft_id=https%3A%2F%2Flink.aps.org%2Fdoi%2F10.1103%2FPhysRev.28.1049&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADavisson%E2%80%93Germer+experiment" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAlpert1953" class="citation journal cs1">Alpert, D. (1953). <a rel="nofollow" class="external text" href="https://pubs.aip.org/aip/jap/article/24/7/860-876/160517">"New Developments in the Production and Measurement of Ultra High Vacuum"</a>. <i>Journal of Applied Physics</i>. <b>24</b> (7): <span class="nowrap">860–</span>876. <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/1953JAP....24..860A">1953JAP....24..860A</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%2F1.1721395">10.1063/1.1721395</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/0021-8979">0021-8979</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Applied+Physics&rft.atitle=New+Developments+in+the+Production+and+Measurement+of+Ultra+High+Vacuum&rft.volume=24&rft.issue=7&rft.pages=%3Cspan+class%3D%22nowrap%22%3E860-%3C%2Fspan%3E876&rft.date=1953&rft.issn=0021-8979&rft_id=info%3Adoi%2F10.1063%2F1.1721395&rft_id=info%3Abibcode%2F1953JAP....24..860A&rft.aulast=Alpert&rft.aufirst=D.&rft_id=https%3A%2F%2Fpubs.aip.org%2Faip%2Fjap%2Farticle%2F24%2F7%2F860-876%2F160517&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADavisson%E2%80%93Germer+experiment" class="Z3988"></span></span> </li> <li id="cite_note-VanHove-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-VanHove_17-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFM._A._Van_HoveW._H._WeinbergC._M._Chan1986" class="citation book cs1">M. A. Van Hove; W. H. Weinberg; C. M. Chan (1986). <span class="id-lock-limited" title="Free access subject to limited trial, subscription normally required"><a rel="nofollow" class="external text" href="https://archive.org/details/lowenergyelectro00hove"><i>Low-Energy Electron Diffraction</i></a></span>. Springer-Verlag, Berlin Heidelberg New York. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/lowenergyelectro00hove/page/n7">1</a>–27, <span class="nowrap">46–</span>89, <span class="nowrap">92–</span>124, <span class="nowrap">145–</span>172. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fmaco.19870380711">10.1002/maco.19870380711</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-16262-9" title="Special:BookSources/978-3-540-16262-9"><bdi>978-3-540-16262-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Low-Energy+Electron+Diffraction&rft.pages=1-27%2C+%3Cspan+class%3D%22nowrap%22%3E46-%3C%2Fspan%3E89%2C+%3Cspan+class%3D%22nowrap%22%3E92-%3C%2Fspan%3E124%2C+%3Cspan+class%3D%22nowrap%22%3E145-%3C%2Fspan%3E172&rft.pub=Springer-Verlag%2C+Berlin+Heidelberg+New+York&rft.date=1986&rft_id=info%3Adoi%2F10.1002%2Fmaco.19870380711&rft.isbn=978-3-540-16262-9&rft.au=M.+A.+Van+Hove&rft.au=W.+H.+Weinberg&rft.au=C.+M.+Chan&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Flowenergyelectro00hove&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADavisson%E2%80%93Germer+experiment" class="Z3988"></span></span> </li> </ol></div> <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=Davisson%E2%80%93Germer_experiment&action=edit&section=6" 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"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Davisson-Germer_experiment" class="extiw" title="commons:Category:Davisson-Germer experiment">Davisson-Germer experiment</a></span>.</div></div> </div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFR._Nave" class="citation web cs1">R. 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.navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Quantum_mechanics332" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template: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_mechanics332" style="font-size:114%;margin:0 4em"><a href="/wiki/Quantum_mechanics" title="Quantum mechanics">Quantum mechanics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Background</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Introduction_to_quantum_mechanics" title="Introduction to quantum mechanics">Introduction</a></li> <li><a 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 class="mw-selflink selflink">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> 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