Ehrenfest theorem
E735839
The Ehrenfest theorem is a fundamental result in quantum mechanics that links the time evolution of expectation values of quantum observables to the corresponding classical equations of motion, thereby bridging quantum and classical physics.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Ehrenfest theorem canonical | 3 |
How this entity was disambiguated
This entity first appeared as the object of triple T8490717 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Ehrenfest theorem Context triple: [Paul Ehrenfest, notableWork, Ehrenfest theorem]
-
A.
Liouville–von Neumann equation
The Liouville–von Neumann equation is the fundamental quantum-mechanical evolution equation governing the time dependence of the density operator, generalizing the Schrödinger equation to mixed states and open-system dynamics.
-
B.
Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
-
C.
Schrödinger equation
The Schrödinger equation is the fundamental equation of non-relativistic quantum mechanics that governs how the quantum state of a physical system evolves over time.
-
D.
Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
-
E.
H-theorem
The H-theorem is Boltzmann’s foundational result in statistical mechanics that explains the irreversible increase of entropy in a gas from time-reversible microscopic dynamics, providing a key link between mechanics and the second law of thermodynamics.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Ehrenfest theorem Target entity description: The Ehrenfest theorem is a fundamental result in quantum mechanics that links the time evolution of expectation values of quantum observables to the corresponding classical equations of motion, thereby bridging quantum and classical physics.
-
A.
Liouville–von Neumann equation
The Liouville–von Neumann equation is the fundamental quantum-mechanical evolution equation governing the time dependence of the density operator, generalizing the Schrödinger equation to mixed states and open-system dynamics.
-
B.
Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
-
C.
Schrödinger equation
The Schrödinger equation is the fundamental equation of non-relativistic quantum mechanics that governs how the quantum state of a physical system evolves over time.
-
D.
Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
-
E.
H-theorem
The H-theorem is Boltzmann’s foundational result in statistical mechanics that explains the irreversible increase of entropy in a gas from time-reversible microscopic dynamics, providing a key link between mechanics and the second law of thermodynamics.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf | quantum mechanics theorem ⓘ |
| appliesTo |
expectation values
ⓘ
general Hermitian operators ⓘ momentum operator ⓘ position operator ⓘ quantum observables ⓘ |
| assumes |
self-adjoint operators for observables
ⓘ
sufficiently well-behaved wavefunctions ⓘ |
| bridges | quantum mechanics and classical mechanics ⓘ |
| canBeGeneralizedTo | relativistic quantum mechanics ⓘ |
| category | theorems in quantum mechanics ⓘ |
| clarifies | relationship between operator equations and classical laws ⓘ |
| concerns | expectation value dynamics ⓘ |
| describes | time evolution of expectation values of observables ⓘ |
| field | quantum mechanics ⓘ |
| hasDomain | nonrelativistic quantum mechanics ⓘ |
| hasFormula | d⟨A⟩/dt = (i/ħ)⟨[H,A]⟩ + ⟨∂A/∂t⟩ ⓘ |
| historicalPeriod | early 20th century ⓘ |
| holdsIn |
Heisenberg picture
ⓘ
Schrödinger picture ⓘ |
| implies |
d⟨p⟩/dt = −⟨∂V/∂x⟩ for potential V(x)
ⓘ
d⟨x⟩/dt = ⟨p⟩/m for a particle of mass m ⓘ |
| importance | fundamental for understanding quantum–classical correspondence ⓘ |
| involves |
Hamiltonian operator
ⓘ
commutators ⓘ |
| isUsedFor |
connecting quantum dynamics to classical trajectories
ⓘ
interpretation of quantum motion ⓘ semiclassical analysis ⓘ |
| mathematicallyExpressedIn |
Hilbert space framework
ⓘ
operator formalism ⓘ |
| mayFailToGive | exact classical motion for highly nonclassical states ⓘ |
| namedAfter | Paul Ehrenfest ⓘ |
| relatedTo |
Heisenberg equation of motion
ⓘ
Heisenberg uncertainty principle ⓘ
linked to:
uncertainty principle
Schrödinger equation of motion ⓘ
linked to:
Schrödinger equation
correspondence principle ⓘ |
| relates |
quantum expectation values to classical equations of motion
ⓘ
time derivative of expectation value to commutator with Hamiltonian ⓘ |
| shows | classical equations emerge from quantum mechanics in expectation values ⓘ |
| specialCase | Newton’s second law in expectation value form ⓘ |
| typeOf | dynamical theorem ⓘ |
| usedIn |
atomic physics
ⓘ
condensed matter physics ⓘ molecular dynamics with quantum effects ⓘ quantum chemistry ⓘ |
| uses |
Heisenberg equation of motion
ⓘ
Schrödinger equation ⓘ |
| validUnder | smooth potentials ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Ehrenfest theorem Description of subject: The Ehrenfest theorem is a fundamental result in quantum mechanics that links the time evolution of expectation values of quantum observables to the corresponding classical equations of motion, thereby bridging quantum and classical physics.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.