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Theorem

Ehrenfest Theorem

Mathematical Physics

The Ehrenfest Theorem relates the time evolution of the expectation values of position and momentum in quantum mechanics to the classical equations of motion, showing that these expectation values obey Newton's second law when the potential is evaluated at the expectation value of position. Named for Paul Ehrenfest, it is a foundational result clarifying the correspondence between quantum and classical mechanics.

Facts
Statement
The Ehrenfest theorem relates the time derivative of the expectation values of the position and momentum operators x and p to the expectation value of the force. 1
Proof Year
1927 1
Classification
Statement Form
Identity or Equation 1
Connections

Has Statement Form

Equation, Concepts

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

Identity, Concepts

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

Sources
1. Ehrenfest theorem, Wikipedia
  • Lead section
    The Ehrenfest theorem, named after Austrian theoretical physicist Paul Ehrenfest, relates the time derivative of the expectation values of the position and momentum operators x and p to the expectation value of the force.
  • References section
    Ehrenfest, P. (1927). Bemerkung über die angenäherte Gültigkeit der klassischen Mechanik innerhalb der Quantenmechanik. Zeitschrift für Physik. 45 (7-8): 455-457.
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