Lippmann–Schwinger equation
E371027
The Lippmann–Schwinger equation is an integral equation in quantum scattering theory that reformulates the Schrödinger equation to describe how incoming waves are transformed into scattered waves by a potential.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Lippmann–Schwinger equation canonical | 5 |
How this entity was disambiguated
This entity first appeared as the object of triple T3576808 — 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: Lippmann–Schwinger equation Context triple: [Bethe–Salpeter equation, relatedTo, Lippmann–Schwinger equation]
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A.
Bethe–Salpeter equation
The Bethe–Salpeter equation is a relativistic quantum field theory equation that describes bound states of two interacting particles, such as electron–hole pairs in quantum electrodynamics.
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B.
Tomonaga–Schwinger equation
The Tomonaga–Schwinger equation is a relativistic generalization of the Schrödinger equation that formulates quantum field evolution on arbitrary spacelike hypersurfaces, forming a key part of covariant quantum field theory.
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C.
Born approximation in scattering theory
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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D.
Schwinger–Dyson equations
The Schwinger–Dyson equations are a set of integral equations in quantum field theory that relate correlation functions and encode the full dynamics of a quantum field.
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E.
Gelfand–Levitan theory
Gelfand–Levitan theory is a foundational framework in inverse spectral theory that reconstructs differential operators or potentials from their spectral data using integral equations.
- 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: Lippmann–Schwinger equation Target entity description: The Lippmann–Schwinger equation is an integral equation in quantum scattering theory that reformulates the Schrödinger equation to describe how incoming waves are transformed into scattered waves by a potential.
-
A.
Bethe–Salpeter equation
The Bethe–Salpeter equation is a relativistic quantum field theory equation that describes bound states of two interacting particles, such as electron–hole pairs in quantum electrodynamics.
-
B.
Tomonaga–Schwinger equation
The Tomonaga–Schwinger equation is a relativistic generalization of the Schrödinger equation that formulates quantum field evolution on arbitrary spacelike hypersurfaces, forming a key part of covariant quantum field theory.
-
C.
Born approximation in scattering theory
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.
-
D.
Schwinger–Dyson equations
The Schwinger–Dyson equations are a set of integral equations in quantum field theory that relate correlation functions and encode the full dynamics of a quantum field.
-
E.
Gelfand–Levitan theory
Gelfand–Levitan theory is a foundational framework in inverse spectral theory that reconstructs differential operators or potentials from their spectral data using integral equations.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
equation in quantum mechanics
ⓘ
integral equation ⓘ scattering theory equation ⓘ |
| appliesTo |
stationary scattering states
ⓘ
time-independent scattering ⓘ |
| assumes | short-range or well-behaved potentials for standard derivations ⓘ |
| characterizedBy |
energy-dependent Green’s function
ⓘ
integral over intermediate coordinates or momenta ⓘ |
| contains |
free Green’s operator G_0^{(±)}(E)
ⓘ
free Hamiltonian H_0 ⓘ full Hamiltonian H = H_0 + V ⓘ interaction potential V ⓘ |
| defines |
incoming scattering states
ⓘ
outgoing scattering states ⓘ |
| describes | quantum scattering from a potential ⓘ |
| field |
quantum mechanics
ⓘ
quantum scattering theory ⓘ |
| hasForm | |ψ^{(±)}⟩ = |φ⟩ + G_0^{(±)} V |ψ^{(±)}⟩ ⓘ |
| hasSolutionType | integral equation for wavefunctions ⓘ |
| implies | asymptotic boundary conditions for scattering states ⓘ |
| mathematicalForm | ψ^{(±)}(r) = φ(r) + ∫ G_0^{(±)}(r,r';E) V(r') ψ^{(±)}(r') d^3r' ⓘ |
| namedAfter |
Bernard A. Lippmann
NERFINISHED
ⓘ
Julian Schwinger ⓘ |
| publishedIn | Physical Review ⓘ |
| reformulates |
Schrödinger equation
ⓘ
surface form:
time-independent Schrödinger equation
|
| relatedTo |
Schwinger–Dyson equations
ⓘ
surface form:
Dyson equation
Møller operators ⓘ S-matrix ⓘ resolvent formalism in operator theory ⓘ |
| relates |
incoming wave
ⓘ
scattered wave ⓘ scattering potential ⓘ |
| usedFor |
Born approximation
ⓘ
Born expansion of Green’s function ⓘ
surface form:
Born series expansion
construction of scattering states from free states ⓘ derivation of differential cross sections ⓘ derivation of scattering amplitudes ⓘ derivation of the T-matrix ⓘ multiple scattering theory ⓘ |
| usedIn |
atomic scattering theory
ⓘ
molecular scattering theory ⓘ nonrelativistic quantum mechanics ⓘ nuclear scattering theory ⓘ potential scattering ⓘ quantum chemistry scattering calculations ⓘ |
| uses |
Green’s function
ⓘ
resolvent operator ⓘ |
| yearProposed | 1950 ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: Lippmann–Schwinger equation Description of subject: The Lippmann–Schwinger equation is an integral equation in quantum scattering theory that reformulates the Schrödinger equation to describe how incoming waves are transformed into scattered waves by a potential.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.