Brillouin–Wigner perturbation theory

E33422

Brillouin–Wigner perturbation theory is a formulation of quantum mechanical perturbation theory that uses an energy-dependent effective Hamiltonian to obtain improved approximations to eigenvalues and eigenstates.

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Generate an image of Brillouin–Wigner perturbation theory (Brillouin–Wigner perturbation theory is a formulation of quantum mechanical perturbation theory that uses an energy-dependent effective Hamiltonian to obtain improved approximations to eigenvalues and eigenstates.)

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Statements (41)

Predicate Object
instanceOf perturbation theory ⓘ
quantum mechanical formalism ⓘ
advantage can improve convergence of perturbation series in some problems ⓘ
aimsTo obtain improved approximations to eigenstates ⓘ
obtain improved approximations to eigenvalues ⓘ
appliedIn nuclear shell-model calculations ⓘ
appliesTo discrete spectra ⓘ
time-independent Hamiltonians ⓘ
assumes existence of a solvable unperturbed Hamiltonian ⓘ
basedOn partition of Hamiltonian into unperturbed and perturbation parts ⓘ
category approximation method in quantum theory ⓘ
characteristic energy appearing on both sides of the eigenvalue equation ⓘ
comparedTo Rayleigh–Schrödinger perturbation theory ⓘ
contrastWith Rayleigh–Schrödinger perturbation theory using energy-independent effective Hamiltonian ⓘ
developedIn 20th century ⓘ
feature nonlinear dependence of energy corrections on the exact energy ⓘ
field quantum mechanics ⓘ
focusesOn corrections to eigenvalues and eigenvectors of the unperturbed Hamiltonian ⓘ
formalismType time-independent perturbation theory ⓘ
framework Hilbert space of quantum states ⓘ
goal improve accuracy beyond low-order perturbation results ⓘ
involves projection operators onto model space and complementary space ⓘ
limitation leads to implicit equations for energies ⓘ
requires self-consistent solution for eigenvalues ⓘ
mathematicalForm series expansion in powers of the perturbation ⓘ
namedAfter Eugene Wigner ⓘ
Léon Brillouin ⓘ
relatedConcept Brillouin–Wigner expansion ⓘ
quasi-degenerate perturbation theory ⓘ
relatedTo Feshbach projection formalism ⓘ
effective Hamiltonian methods ⓘ
requires choice of model space ⓘ
definition of projection operators ⓘ
usedFor bound-state problems in quantum mechanics ⓘ
many-body quantum systems ⓘ
usedIn atomic physics ⓘ
condensed matter physics ⓘ
molecular physics ⓘ
usedToDerive effective interactions in model spaces ⓘ
uses energy-dependent effective Hamiltonian ⓘ
yields energy-dependent effective Hamiltonian in model space ⓘ

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Referenced by (5)

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

Rayleigh–Schrödinger perturbation theory → relatedTo → Brillouin–Wigner perturbation theory ⓘ
Brillouin–Wigner perturbation theory → relatedConcept → quasi-degenerate perturbation theory ⓘ
linked to: Brillouin–Wigner perturbation theory
Brillouin–Wigner perturbation theory → relatedConcept → Brillouin–Wigner expansion ⓘ
linked to: Brillouin–Wigner perturbation theory
Léon Brillouin → notableConcept → Brillouin–Wigner perturbation theory ⓘ
Löwdin partitioning → relatedTo → Brillouin–Wigner perturbation theory ⓘ