Rayleigh–Schrödinger perturbation theory

E5100

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.

AI illustration

How this image was made

AI-generated illustration of Rayleigh–Schrödinger perturbation theory

This AI-generated illustration was produced by black-forest-labs/FLUX.2-dev (1024x1024) from a prompt written by openai/gpt-oss-120b from the entity's label + description.

Prompt

Generate an image of Rayleigh–Schrödinger 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.)

All labels observed (3)

How this entity was disambiguated

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 degenerate Rayleigh–Schrödinger perturbation theory ⓘ
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 ⓘ

How these facts were elicited

Referenced by (4)

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

Feynman–Hellmann theorem → relatedTo → Rayleigh–Schrödinger perturbation theory ⓘ
Rayleigh–Schrödinger perturbation theory → hasVariant → non-degenerate Rayleigh–Schrödinger perturbation theory ⓘ
linked to: Rayleigh–Schrödinger perturbation theory
Rayleigh–Schrödinger perturbation theory → hasVariant → degenerate Rayleigh–Schrödinger perturbation theory ⓘ
linked to: Rayleigh–Schrödinger perturbation theory
Brillouin–Wigner perturbation theory → comparedTo → Rayleigh–Schrödinger perturbation theory ⓘ