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.

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All labels observed (5)

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

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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.

Max Born knownFor Born approximation in scattering theory
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
Born series relatedConcept Born approximation in scattering theory
this entity surface form: Born approximation
Born expansion of Green’s function relatedTo Born approximation in scattering theory
this entity surface form: Born approximation