Ehrenfest theorem
theorem that the time evolution of the expectation value of a quantum observable is proportional to that of the commutator between the observable and the Hamiltonian (plus that of any explicit time dependence of the operator, if any)
| rdfs:label |
"Ehrenfest theorem"@en
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skos:alt |
"Ehrenfest's theorem"@en
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| schema:description |
"theorem that the time evolution of the expectation value of a quantum observable is proportional to that of the commutator between the observable and the Hamiltonian (plus that of any explicit time dependence of the operator, if any)"@en
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schema:date |
"2025-08-29T15:34:45+00:00"^^xsd:dateTime |
| schema:version | 2398123439 |
| wikibase:identifiers | 5 |
| wikibase:sitelinks | 29 |
| wikibase:statements | 17 |
| p:P1051 | wd:statement/Q908669-4058B018-A742-4E9C-B2B5-F45B7177CF42 |
| p:P138 | wd:statement/q908669-8437F853-CA4F-4FD0-B938-E022D39BF879 |
| p:P18 | wd:statement/Q908669-434e911f-4b45-0e8e-25d4-d6cbc9766d54 |
| p:P2534 | wd:statement/Q908669-526d48c1-4c45-7cfd-8d8f-c44b12a4be8c |
| p:P31 | wd:statement/Q908669-CB79F39F-06C1-4773-A6C3-3026C5904FED |
| p:P373 | wd:statement/Q908669-1eb8db56-4c15-433e-b264-cb5c32508e1d |
| p:P4839 | wd:statement/Q908669-9A29E171-02E7-458E-B5AA-CC083C92DFCC |
| p:P5064 | wd:statement/Q908669-24efd9a6-415e-2b2d-fdb0-1b4dedd6e862 |
| p:P6104 | wd:statement/Q908669-39BA7A77-34E3-4B62-BAF0-3DD13E4FD420 |
| p:P6366 | wd:statement/Q908669-FFF94F27-4325-4898-BFA9-F4604D653B35 |
| p:P646 | wd:statement/Q908669-C6EDE6CF-B869-42C8-89D7-AA078337021C |
| p:P7235 | wd:statement/Q908669-24f5a290-4b14-9cf4-6ee1-23fd17b20c86 |
| wd:statement/Q908669-2ad22cb7-4ae2-34e8-1259-7dcc47844d36 | |
| wd:statement/Q908669-41cd304f-46c1-651a-d26b-26dcfa5f9e9d | |
| wd:statement/Q908669-7910a2dc-43e5-f400-fb5a-dd4603a89b33 | |
| wd:statement/Q908669-7aacfa4e-492d-adad-f417-af9272b391bd | |
| wd:statement/Q908669-d653fd99-4cc3-50a2-36fe-d88da9aaa37d | |
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p:direct- |
<https:/ |
| wdt:P1051 | "3575" |
| wdt:P138 | Paul Ehrenfest |
| wdt:P18 |
<http:/ |
| wdt:P2534 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">d</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">d</mi></mrow><mi>t</mi></mrow></mrow></mfrac></mrow><mo stretchy="false">⟨</mo><mi>A</mi><mo stretchy="false">⟩</mo><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">i</mi></mrow><mi alternate="1">ℏ</mi></mrow></mrow></mfrac></mrow><mo stretchy="false">⟨</mo><mo stretchy="false">[</mo><mi>A</mi><mo>,</mo><mi>H</mi><mo stretchy="false">]</mo><mo stretchy="false">⟩</mo><mo stretchy="false">+</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>A</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>t</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P31 | theorem |
| wdt:P373 | "Ehrenfest theorem" |
| wdt:P4839 | "Entity["PhysicalEffect", "EhrenfestTheorem"]" |
| wdt:P5064 | "EhrenfestTheorem" |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "172314311" |
| wdt:P646 | "/m/07pv44" |
| wdt:P7235 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi alternate="1">ℏ</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>A</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>H</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mo stretchy="false">⟨</mo><mo stretchy="false">⟩</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mo stretchy="false">[</mo><mo>,</mo><mo stretchy="false">]</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">i</mi></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
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