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.
All labels observed (3)
| Label | Occurrences |
|---|---|
| WKB approximation canonical | 6 |
| JWKB approximation | 1 |
| Wentzel–Kramers–Brillouin approximation | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T9700401 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: WKB approximation Context triple: [Sommerfeld quantization rules, relatedTo, WKB approximation]
-
A.
WKB
WKB (Well-Known Binary) is a compact binary format used to represent geometric objects in spatial databases and GIS systems.
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B.
Condon approximation
The Condon approximation is a simplifying assumption in molecular spectroscopy that treats electronic transition dipole moments as independent of nuclear coordinates, enabling easier calculation of vibronic transition intensities.
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C.
Born–Oppenheimer approximation
The Born–Oppenheimer approximation is a fundamental method in molecular quantum mechanics that simplifies calculations by treating nuclear motion as much slower than electronic motion, allowing their behaviors to be separated.
-
D.
Migdal approximation
The Migdal approximation is a theoretical simplification in many-body physics that neglects vertex corrections in electron-phonon interactions, justified when phonon energies are much smaller than electronic energies.
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E.
Weyl quantization
Weyl quantization is a mathematical procedure in quantum mechanics that systematically associates classical observables with quantum operators in a symmetric and coordinate-independent way.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: WKB approximation Target entity description: 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.
-
A.
WKB
WKB (Well-Known Binary) is a compact binary format used to represent geometric objects in spatial databases and GIS systems.
-
B.
Condon approximation
The Condon approximation is a simplifying assumption in molecular spectroscopy that treats electronic transition dipole moments as independent of nuclear coordinates, enabling easier calculation of vibronic transition intensities.
-
C.
Born–Oppenheimer approximation
The Born–Oppenheimer approximation is a fundamental method in molecular quantum mechanics that simplifies calculations by treating nuclear motion as much slower than electronic motion, allowing their behaviors to be separated.
-
D.
Migdal approximation
The Migdal approximation is a theoretical simplification in many-body physics that neglects vertex corrections in electron-phonon interactions, justified when phonon energies are much smaller than electronic energies.
-
E.
Weyl quantization
Weyl quantization is a mathematical procedure in quantum mechanics that systematically associates classical observables with quantum operators in a symmetric and coordinate-independent way.
- F. None of above. chosen
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
ⓘ
linked to:
WKB approximation
|
| generalizedBy |
phase-integral method
ⓘ
uniform WKB approximation ⓘ |
| hasConcept |
Maslov index
ⓘ
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
ⓘ
Hendrik Anthony Kramers ⓘ Léon Brillouin ⓘ |
| relatedMethod |
JWKB approximation
ⓘ
linked to:
WKB approximation
Langer modification ⓘ |
| relatesTo |
Hamilton–Jacobi equation
ⓘ
classical trajectories ⓘ eikonal approximation ⓘ geometric optics ⓘ |
| usedFor |
Bohr–Sommerfeld quantization
ⓘ
linked to:
Sommerfeld quantization rules
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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: WKB approximation Description of subject: 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.
Referenced by (8)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: WKB approximation
linked to: WKB approximation