WKB approximation
E814350
approximation method in quantum mechanics
asymptotic analysis technique
semiclassical approximation method
The WKB approximation is a semiclassical method in quantum mechanics that provides approximate solutions to the Schrödinger equation by treating wavefunctions in analogy with classical trajectories, especially in slowly varying potentials.
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
approximation method in quantum mechanics
ⓘ
asymptotic analysis technique ⓘ semiclassical approximation method ⓘ |
| appliedIn |
atomic physics
ⓘ
molecular physics ⓘ nuclear physics ⓘ quantum field theory semiclassical analysis ⓘ |
| appliesTo |
multidimensional quantum systems
ⓘ
one-dimensional Schrödinger equation ⓘ |
| approximates |
wavefunction as exponential of an action-like function
ⓘ
wavefunction phase using classical action ⓘ |
| assumes |
large quantum numbers
ⓘ
slowly varying potential compared to de Broglie wavelength ⓘ small effective Planck constant limit ⓘ |
| basedOn |
correspondence principle
ⓘ
semiclassical limit of quantum mechanics ⓘ |
| expandsIn | powers of Planck constant ħ ⓘ |
| failsNear |
classical turning points
ⓘ
rapidly varying potentials ⓘ |
| field |
asymptotic analysis
ⓘ
mathematical physics ⓘ quantum mechanics ⓘ |
| fullName | Wentzel–Kramers–Brillouin approximation NERFINISHED ⓘ |
| generalizedBy |
phase-integral method
ⓘ
uniform WKB approximation ⓘ |
| hasConcept |
Maslov index
NERFINISHED
ⓘ
classically allowed region ⓘ classically forbidden region ⓘ connection formulas at turning points ⓘ phase loss at turning points ⓘ turning point ⓘ |
| hasForm | ψ(x) ≈ A(x) exp( i S(x) / ħ ) ⓘ |
| isValidWhen | potential varies on length scales large compared to local wavelength ⓘ |
| namedAfter |
Gregor Wentzel
NERFINISHED
ⓘ
Hendrik Anthony Kramers NERFINISHED ⓘ Léon Brillouin NERFINISHED ⓘ |
| relatedMethod |
JWKB approximation
NERFINISHED
ⓘ
Langer modification NERFINISHED ⓘ |
| relatesTo |
Hamilton–Jacobi equation
NERFINISHED
ⓘ
classical trajectories ⓘ eikonal approximation ⓘ geometric optics ⓘ |
| usedFor |
Bohr–Sommerfeld quantization
NERFINISHED
ⓘ
analysis of slowly varying potentials ⓘ approximate solutions of the time-dependent Schrödinger equation ⓘ approximate solutions of the time-independent Schrödinger equation ⓘ barrier penetration problems ⓘ bound-state quantization conditions ⓘ semiclassical analysis of quantum systems ⓘ tunneling probability calculations ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.