Born approximation in scattering theory
E75606
The Born approximation in scattering theory is a perturbative method used in quantum mechanics to approximate scattering amplitudes by treating the interaction potential as a small perturbation to a free-particle wave.
All labels observed (5)
| Label | Occurrences |
|---|---|
| Born approximation | 2 |
| Born approximation in scattering theory canonical | 1 |
| Lippmann–Schwinger equation | 1 |
| first Born approximation | 1 |
| second Born approximation | 1 |
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
approximation method in quantum scattering theory
ⓘ
perturbative method in quantum mechanics ⓘ |
| appliesTo |
elastic scattering
ⓘ
inelastic scattering ⓘ |
| approximates |
scattering amplitude
ⓘ
transition matrix element (T-matrix) ⓘ |
| approximationType | single-interaction approximation ⓘ |
| assumes |
incident wave is a plane wave
ⓘ
interaction potential is weak ⓘ scattering can be treated as a perturbation of free motion ⓘ |
| basedOn |
Born approximation in scattering theory
self-linksurface differs
ⓘ
surface form:
Lippmann–Schwinger equation
time-independent perturbation theory ⓘ |
| canBeGeneralizedTo | relativistic scattering in quantum field theory ⓘ |
| domain | nonrelativistic quantum field description of scattering ⓘ |
| expresses | scattering amplitude as matrix element of potential between plane waves ⓘ |
| failsWhen |
low-energy scattering from long-range potentials
ⓘ
near bound-state or resonance energies ⓘ potential is strong ⓘ |
| hasFormulation |
Born approximation in scattering theory
self-linksurface differs
ⓘ
surface form:
first Born approximation
Born approximation in scattering theory self-linksurface differs ⓘ
surface form:
second Born approximation
|
| historicallyIntroducedBy | Max Born ⓘ |
| influenced | development of modern scattering theory ⓘ |
| mathematicallyInvolves |
Fourier transform of interaction potential
ⓘ
Green’s function of free particle ⓘ |
| namedAfter | Max Born ⓘ |
| neglects | multiple scattering events beyond first order ⓘ |
| order | first order in the interaction potential ⓘ |
| relatedConcept |
Born–Oppenheimer approximation (by name only, conceptually distinct)
ⓘ
distorted-wave Born approximation ⓘ |
| relatedTo |
Born expansion of Green’s function
ⓘ
Born series ⓘ |
| relates | differential cross section to Fourier transform of potential ⓘ |
| requires | knowledge of interaction potential in coordinate space ⓘ |
| usedFor |
X-ray scattering calculations
ⓘ
calculating scattering cross sections ⓘ electron scattering calculations ⓘ neutron scattering calculations ⓘ optical scattering in weakly inhomogeneous media ⓘ |
| usedIn |
high-energy scattering regime
ⓘ
inverse scattering problems under weak-scattering assumption ⓘ nonrelativistic quantum mechanics ⓘ partial-wave analysis of scattering ⓘ potential scattering ⓘ quantum scattering theory ⓘ |
| validWhen |
scattering potential is small compared to kinetic energy
ⓘ
single scattering dominates over multiple scattering ⓘ |
| yearProposed | 1926 ⓘ |
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: Born approximation in scattering theory Description of subject: The Born approximation in scattering theory is a perturbative method used in quantum mechanics to approximate scattering amplitudes by treating the interaction potential as a small perturbation to a free-particle wave.
Referenced by (6)
Full triples — surface form annotated when it differs from this entity's canonical label.
Born approximation in scattering theory
→
basedOn
→
Born approximation in scattering theory
self-linksurface differs
ⓘ
subject surface form:
Born approximation
this entity surface form:
Lippmann–Schwinger equation
Born approximation in scattering theory
→
hasFormulation
→
Born approximation in scattering theory
self-linksurface differs
ⓘ
subject surface form:
Born approximation
this entity surface form:
first Born approximation
Born approximation in scattering theory
→
hasFormulation
→
Born approximation in scattering theory
self-linksurface differs
ⓘ
subject surface form:
Born approximation
this entity surface form:
second Born approximation
this entity surface form:
Born approximation
this entity surface form:
Born approximation