Feynman–Hellmann theorem
E1162
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.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Feynman–Hellmann theorem canonical | 2 |
| Hellmann–Feynman force theorem | 1 |
| Hellmann–Feynman theorem | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T26867 — 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: Feynman–Hellmann theorem Context triple: [Richard Feynman, knownFor, Feynman–Hellmann theorem]
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A.
Oppenheimer–Phillips process
The Oppenheimer–Phillips process is a nuclear reaction mechanism in which a deuteron interacting with a target nucleus effectively transfers its neutron while the proton is repelled, enabling certain reactions to occur at lower energies than would otherwise be required.
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B.
Richard Feynman
Richard Feynman was a pioneering American theoretical physicist renowned for his work in quantum electrodynamics, his influential teaching, and his popular science writings.
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C.
Differential analyzer
The Differential Analyzer is an early analog mechanical computer designed to solve differential equations using interconnected rotating shafts and wheels.
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D.
Nash embedding theorem
The Nash embedding theorem is a fundamental result in differential geometry that shows any Riemannian manifold can be isometrically embedded into some Euclidean space, thereby realizing abstract curved spaces as concrete subsets of standard Euclidean space.
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E.
Theodor
Theodor "Ted" Nelson is an American pioneer of information technology best known for coining the term "hypertext" and envisioning global hyperlinked document systems.
- 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: Feynman–Hellmann theorem Target entity description: 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.
-
A.
Oppenheimer–Phillips process
The Oppenheimer–Phillips process is a nuclear reaction mechanism in which a deuteron interacting with a target nucleus effectively transfers its neutron while the proton is repelled, enabling certain reactions to occur at lower energies than would otherwise be required.
-
B.
Richard Feynman
Richard Feynman was a pioneering American theoretical physicist renowned for his work in quantum electrodynamics, his influential teaching, and his popular science writings.
-
C.
Differential analyzer
The Differential Analyzer is an early analog mechanical computer designed to solve differential equations using interconnected rotating shafts and wheels.
-
D.
Nash embedding theorem
The Nash embedding theorem is a fundamental result in differential geometry that shows any Riemannian manifold can be isometrically embedded into some Euclidean space, thereby realizing abstract curved spaces as concrete subsets of standard Euclidean space.
-
E.
Theodor
Theodor "Ted" Nelson is an American pioneer of information technology best known for coining the term "hypertext" and envisioning global hyperlinked document systems.
- F. None of above. chosen
Statements (41)
| Predicate | Object |
|---|---|
| instanceOf |
quantum mechanics theorem
ⓘ
theorem in physics ⓘ |
| appliesTo |
Hamiltonians depending on an external parameter
ⓘ
Hermitian operators ⓘ non-degenerate energy eigenstates ⓘ time-independent Hamiltonians ⓘ |
| assumes |
differentiable dependence of the Hamiltonian on the parameter
ⓘ
normalized eigenstates of the Hamiltonian ⓘ |
| category |
eponymous theorems in physics
ⓘ
theorems in quantum mechanics ⓘ |
| clarifies | how changes in Hamiltonian parameters affect observable energies ⓘ |
| context | eigenvalue problems of parameter-dependent operators ⓘ |
| describes | relationship between parameter derivatives of energy eigenvalues and expectation values of Hamiltonian derivatives ⓘ |
| field | quantum mechanics ⓘ |
| hasGeneralization |
applications in relativistic quantum field theory
ⓘ
extensions to degenerate eigenvalues ⓘ extensions to multiple parameters ⓘ |
| mathematicalForm | dE_n/dλ = ⟨ψ_n| ∂H/∂λ |ψ_n⟩ ⓘ |
| namedAfter |
Hans Hellmann
ⓘ
Richard Feynman ⓘ
surface form:
Richard P. Feynman
|
| relatedTo |
Feynman–Hellmann theorem
self-linksurface differs
ⓘ
surface form:
Hellmann–Feynman force theorem
Rayleigh–Schrödinger perturbation theory ⓘ variational principle in quantum mechanics ⓘ |
| relates |
derivative of an energy eigenvalue with respect to a parameter
ⓘ
expectation value of the derivative of the Hamiltonian with respect to that parameter ⓘ |
| statement | For an eigenstate |n(λ)⟩ of H(λ) with eigenvalue E_n(λ), dE_n(λ)/dλ = ⟨n(λ)| ∂H(λ)/∂λ |n(λ)⟩ ⓘ |
| typeOf | eigenvalue perturbation result ⓘ |
| usedFor |
calculating parameter dependence of energy levels
ⓘ
computing derivatives of bound-state energies with respect to coupling constants ⓘ computing derivatives of bound-state energies with respect to external fields ⓘ computing derivatives of bound-state energies with respect to particle masses ⓘ computing forces in quantum systems ⓘ computing response of bound-state energies to changes in coupling constants ⓘ estimating expectation values without explicit wavefunctions ⓘ perturbation theory in quantum mechanics ⓘ |
| usedIn |
atomic physics
ⓘ
condensed matter physics ⓘ lattice quantum chromodynamics ⓘ molecular physics ⓘ nuclear physics ⓘ quantum chemistry ⓘ |
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: Feynman–Hellmann theorem Description of subject: 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.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Hellmann–Feynman force theorem
this entity surface form:
Hellmann–Feynman theorem