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.
Observed surface forms (4)
| Surface form | Occurrences |
|---|---|
| Born approximation | 0 |
| 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 ⓘ |
Referenced by (4)
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