Feynman–Hellmann theorem

E1162

quantum mechanics theorem theorem in physics

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.

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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]

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
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 P. Feynman ⓘ linked to: Richard Feynman
relatedTo	Hellmann–Feynman force theorem ⓘ linked to: Feynman–Hellmann 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

Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

Richard Feynman → knownFor → Feynman–Hellmann theorem ⓘ

Feynman–Hellmann theorem → relatedTo → Hellmann–Feynman force theorem ⓘ

linked to: Feynman–Hellmann theorem

Hans Hellmann → notableWork → Feynman–Hellmann theorem ⓘ

Hans Hellmann → notableConcept → Hellmann–Feynman theorem ⓘ