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)
Intangible theorem Q908669
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Ehrenfest theorem

Summary

Ehrenfest theorem is a theorem[1]. It draws 183 Wikipedia views per month (theorem category, ranking #132 of 1,306).[2]

Key Facts

  • Ehrenfest theorem's image is recorded as Start of derivation of Ehrenfests theorem (1961608283).jpg[3].
  • Ehrenfest theorem's instance of is recorded as theorem[4].
  • Paul Ehrenfest is named after Ehrenfest theorem[5].
  • Ehrenfest theorem's Commons category is recorded as Ehrenfest theorem[6].
  • Ehrenfest theorem's Freebase ID is recorded as /m/07pv44[7].
  • Ehrenfest theorem's PSH ID is recorded as 3575[8].
  • Ehrenfest theorem's defining formula is recorded as \frac{\mathrm d}{\mathrm dt}\lang A\rang =\frac1{\mathrm i\hbar}\lang[A,H]\rang+\left\lang\frac{\partial A}{\partial t}\right\rang[9].
  • Ehrenfest theorem's Wolfram Language entity code is recorded as Entity["PhysicalEffect", "EhrenfestTheorem"][10].
  • Ehrenfest theorem's World of Physics ID is recorded as EhrenfestTheorem[11].
  • Ehrenfest theorem's maintained by WikiProject is recorded as WikiProject Mathematics[12].
  • Ehrenfest theorem's Microsoft Academic ID is recorded as 172314311[13].
  • Ehrenfest theorem's in defining formula is recorded as A[14].
  • Ehrenfest theorem's in defining formula is recorded as H[15].
  • Ehrenfest theorem's in defining formula is recorded as [,][16].
  • Ehrenfest theorem's in defining formula is recorded as \lang\rang[17].
  • Ehrenfest theorem's in defining formula is recorded as \mathrm i[18].
  • Ehrenfest theorem's in defining formula is recorded as \hbar[19].

Why It Matters

Ehrenfest theorem draws 183 Wikipedia views per month (theorem category, ranking #132 of 1,306).[2] It has Wikipedia articles in 20 language editions, a strong signal of global cultural recognition.[20] It is known by 9 alternative names across languages and contexts.[21]

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [3] . wikidata.org.
  2. [4] . wikidata.org.
  3. [5] . wikidata.org.
  4. [6] . wikidata.org.
  5. [7] . Freebase Data Dumps. wikidata.org.
  6. [8] . wikidata.org.
  7. [9] . wikidata.org.
  8. [10] . wikidata.org.
  9. [11] . wikidata.org.
  10. [12] . wikidata.org.
  11. [13] . wikidata.org.
  12. [14] . wikidata.org.
  13. [15] . wikidata.org.
  14. [16] . wikidata.org.
  15. [17] . wikidata.org.
  16. [18] . wikidata.org.
  17. [19] . wikidata.org.

Class ancestry

  1. [1] . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] . Wikimedia Foundation. dumps.wikimedia.org.
  2. [20] . Wikidata sitelinks. wikidata.org.
  3. [21] . Wikidata aliases. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). Ehrenfest theorem. Retrieved May 3, 2026, from https://4ort.xyz/entity/ehrenfest-theorem
MLA “Ehrenfest theorem.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/ehrenfest-theorem.
BibTeX @misc{4ortxyz_ehrenfest-theorem_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Ehrenfest theorem}}, year = {2026}, url = {https://4ort.xyz/entity/ehrenfest-theorem}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Ehrenfest theorem — https://4ort.xyz/entity/ehrenfest-theorem (retrieved 2026-05-03)

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