Disambiguation evidence for Born approximation in scattering theory via surface form
"Born approximation"
As subject (47)
Triples where this entity appears as subject under the
label "Born approximation".
| Predicate | Object |
|---|---|
| appliesTo | elastic scattering ⓘ |
| appliesTo | inelastic scattering ⓘ |
| approximates | scattering amplitude ⓘ |
| approximates | transition matrix element (T-matrix) ⓘ |
| approximationType | single-interaction approximation ⓘ |
| assumes | incident wave is a plane wave ⓘ |
| assumes | interaction potential is weak ⓘ |
| assumes | scattering can be treated as a perturbation of free motion ⓘ |
| basedOn |
Born approximation in scattering theory
self-linksurface differs
ⓘ
surface form:
Lippmann–Schwinger equation
|
| basedOn | 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 ⓘ |
| failsWhen | near bound-state or resonance energies ⓘ |
| failsWhen | potential is strong ⓘ |
| hasFormulation |
Born approximation in scattering theory
self-linksurface differs
ⓘ
surface form:
first Born approximation
|
| hasFormulation |
Born approximation in scattering theory
self-linksurface differs
ⓘ
surface form:
second Born approximation
|
| historicallyIntroducedBy | Max Born ⓘ |
| influenced | development of modern scattering theory ⓘ |
| instanceOf | approximation method in quantum scattering theory ⓘ |
| instanceOf | perturbative method in quantum mechanics ⓘ |
| mathematicallyInvolves | Fourier transform of interaction potential ⓘ |
| mathematicallyInvolves | 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) ⓘ |
| relatedConcept | distorted-wave Born approximation ⓘ |
| relatedTo | Born expansion of Green’s function ⓘ |
| relatedTo | Born series ⓘ |
| relates | differential cross section to Fourier transform of potential ⓘ |
| requires | knowledge of interaction potential in coordinate space ⓘ |
| usedFor | X-ray scattering calculations ⓘ |
| usedFor | calculating scattering cross sections ⓘ |
| usedFor | electron scattering calculations ⓘ |
| usedFor | neutron scattering calculations ⓘ |
| usedFor | optical scattering in weakly inhomogeneous media ⓘ |
| usedIn | high-energy scattering regime ⓘ |
| usedIn | inverse scattering problems under weak-scattering assumption ⓘ |
| usedIn | nonrelativistic quantum mechanics ⓘ |
| usedIn | partial-wave analysis of scattering ⓘ |
| usedIn | potential scattering ⓘ |
| usedIn | quantum scattering theory ⓘ |
| validWhen | scattering potential is small compared to kinetic energy ⓘ |
| validWhen | single scattering dominates over multiple scattering ⓘ |
| yearProposed | 1926 ⓘ |