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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Observed surface forms (2)

Surface form	Occurrences
Hellmann–Feynman force theorem	1
Hellmann–Feynman theorem	1

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 ⓘ

Referenced by (4)

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

Richard Feynman → knownFor → Feynman–Hellmann theorem ⓘ

Hans Hellmann → notableConcept → Feynman–Hellmann theorem ⓘ

this entity surface form: Hellmann–Feynman theorem

Hans Hellmann → notableWork → Feynman–Hellmann theorem ⓘ

Feynman–Hellmann theorem → relatedTo → Feynman–Hellmann theorem self-linksurface differs ⓘ

this entity surface form: Hellmann–Feynman force theorem