Rayleigh–Schrödinger perturbation theory

E5100

method in quantum mechanics perturbation theory

Rayleigh–Schrödinger perturbation theory is a fundamental method in quantum mechanics for approximating the energies and states of a system by treating interactions as small corrections to an exactly solvable problem.

Jump to: Surface forms Statements Referenced by

Observed surface forms (2)

Surface form	Occurrences
degenerate Rayleigh–Schrödinger perturbation theory	1
non-degenerate Rayleigh–Schrödinger perturbation theory	1

Statements (46)

Predicate	Object
instanceOf	method in quantum mechanics ⓘ perturbation theory ⓘ
appliesTo	bound states ⓘ time-independent quantum systems ⓘ
approximationType	systematic series expansion ⓘ
assumes	exactly solvable unperturbed Hamiltonian ⓘ
computes	energy corrections ⓘ wavefunction corrections ⓘ
contrastedWith	time-dependent perturbation theory ⓘ
developedInContextOf	early quantum mechanics ⓘ
domain	non-relativistic quantum mechanics ⓘ
expandsIn	power series in perturbation parameter ⓘ
failsWhen	energy levels are nearly degenerate without proper treatment ⓘ perturbation is not small ⓘ
field	quantum mechanics ⓘ
generalizes	classical Rayleigh perturbation theory ⓘ
hasVariant	Rayleigh–Schrödinger perturbation theory self-linksurface differs ⓘ surface form: degenerate Rayleigh–Schrödinger perturbation theory Rayleigh–Schrödinger perturbation theory self-linksurface differs ⓘ surface form: non-degenerate Rayleigh–Schrödinger perturbation theory
includes	first-order energy correction ⓘ higher-order corrections ⓘ second-order energy correction ⓘ
influenced	many-body perturbation theory ⓘ quantum chemistry methods ⓘ
isToolFor	approximate solutions of Schrödinger equation ⓘ
mathematicalForm	power series in coupling constant ⓘ
namedAfter	Erwin Schrödinger ⓘ Lord Rayleigh ⓘ
relatedTo	Brillouin–Wigner perturbation theory ⓘ time-independent perturbation theory ⓘ
requires	non-degenerate spectrum for simplest form ⓘ small perturbation compared to level spacings ⓘ
teaches	systematic correction to idealized models ⓘ
treats	interaction as small perturbation ⓘ
usedFor	Stark effect ⓘ Zeeman effect ⓘ atomic spectra calculations ⓘ molecular energy level calculations ⓘ solid-state band structure approximations ⓘ
usedIn	graduate quantum mechanics courses ⓘ undergraduate quantum mechanics courses ⓘ
usesConcept	Hamiltonian operator ⓘ eigenstates ⓘ eigenvalues ⓘ orthonormal basis of unperturbed eigenstates ⓘ projection onto unperturbed states ⓘ
validWhen	perturbation series converges or is asymptotically useful ⓘ

Referenced by (4)

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

Brillouin–Wigner perturbation theory → comparedTo → Rayleigh–Schrödinger perturbation theory ⓘ

Rayleigh–Schrödinger perturbation theory → hasVariant → Rayleigh–Schrödinger perturbation theory self-linksurface differs ⓘ

this entity surface form: non-degenerate Rayleigh–Schrödinger perturbation theory

Rayleigh–Schrödinger perturbation theory → hasVariant → Rayleigh–Schrödinger perturbation theory self-linksurface differs ⓘ

this entity surface form: degenerate Rayleigh–Schrödinger perturbation theory

Feynman–Hellmann theorem → relatedTo → Rayleigh–Schrödinger perturbation theory ⓘ