Schrödinger equation with point interactions
E735006
The Schrödinger equation with point interactions is a quantum-mechanical model in which particles interact via idealized zero-range potentials, typically represented mathematically by Dirac delta functions.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Bethe-Peierls boundary conditions | 1 |
| Schrödinger equation with point interactions canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T8454310 — 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: Schrödinger equation with point interactions Context triple: [Dirac delta function, appearsIn, Schrödinger equation with point interactions]
-
A.
Haag-Ruelle scattering theory
Haag-Ruelle scattering theory is a rigorous framework in quantum field theory that constructs and analyzes scattering states and S-matrix elements from local fields under mathematically precise conditions.
-
B.
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.
-
C.
Rayleigh–Schrödinger perturbation theory
Rayleigh–Schrödinger perturbation theory is a fundamental method in quantum mechanics for approximating the energies and states of a system by treating interactions as small corrections to an exactly solvable problem.
-
D.
Mathematical Foundations of Quantum Mechanics
Mathematical Foundations of Quantum Mechanics is John von Neumann’s landmark 1932 treatise that rigorously formulates quantum theory using functional analysis and operator theory on Hilbert spaces.
-
E.
Lippmann–Schwinger equation
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.
- 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: Schrödinger equation with point interactions Target entity description: The Schrödinger equation with point interactions is a quantum-mechanical model in which particles interact via idealized zero-range potentials, typically represented mathematically by Dirac delta functions.
-
A.
Haag-Ruelle scattering theory
Haag-Ruelle scattering theory is a rigorous framework in quantum field theory that constructs and analyzes scattering states and S-matrix elements from local fields under mathematically precise conditions.
-
B.
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.
-
C.
Rayleigh–Schrödinger perturbation theory
Rayleigh–Schrödinger perturbation theory is a fundamental method in quantum mechanics for approximating the energies and states of a system by treating interactions as small corrections to an exactly solvable problem.
-
D.
Mathematical Foundations of Quantum Mechanics
Mathematical Foundations of Quantum Mechanics is John von Neumann’s landmark 1932 treatise that rigorously formulates quantum theory using functional analysis and operator theory on Hilbert spaces.
-
E.
Lippmann–Schwinger equation
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.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
Schrödinger equation
ⓘ
differential equation with singular potential ⓘ quantum mechanical model ⓘ |
| approximationOf | short-range regular potentials in zero-range limit ⓘ |
| boundaryConditionType |
1/r behavior near interaction in 3D
ⓘ
discontinuity in derivative of wave function in 1D ⓘ logarithmic behavior near interaction in 2D ⓘ |
| dependsOnParameter |
coupling constant of each point interaction
ⓘ
positions of interaction centers ⓘ |
| describes |
bound states generated by localized interactions
ⓘ
quantum particles interacting at points ⓘ scattering by point-like impurities ⓘ |
| field |
functional analysis
ⓘ
mathematical physics ⓘ quantum mechanics ⓘ spectral theory ⓘ |
| governs | time evolution of wave functions with point-like interactions ⓘ |
| hasComponent |
free Schrödinger operator on configuration space minus interaction points
ⓘ
matching conditions for wave function at interaction points ⓘ |
| hasMathematicalForm | (-ħ^2/2m) Δψ + V ψ = E ψ with V a sum of delta functions ⓘ |
| hasProperty |
exactly solvable in many cases
ⓘ
models idealized short-range interactions ⓘ spectrum depends on coupling strengths and positions ⓘ translation invariance broken by interaction locations ⓘ |
| hasSolutionType |
bound states
ⓘ
resonant states ⓘ scattering states ⓘ |
| quantizationType | nonrelativistic ⓘ |
| relatedTo |
Bethe-Peierls boundary conditions
ⓘ
linked to:
Schrödinger equation with point interactions
Krein resolvent formula ⓘ contact interaction ⓘ delta-function potential ⓘ self-adjoint extensions of the Laplacian ⓘ |
| requires |
boundary conditions at interaction points
ⓘ
renormalization of coupling constants in higher dimensions ⓘ self-adjoint extension theory ⓘ |
| spaceDimension |
one-dimensional version
ⓘ
three-dimensional version ⓘ two-dimensional version ⓘ |
| typicalPotentialForm | V(x) = ∑_j α_j δ(x - x_j) ⓘ |
| usedFor |
modeling impurities in quantum wires
ⓘ
modeling quantum dots and point scatterers ⓘ studying bound states induced by localized perturbations ⓘ studying solvable models of scattering theory ⓘ testing renormalization methods in nonrelativistic quantum mechanics ⓘ |
| usesPotentialType |
Dirac delta potential
ⓘ
linked to:
Dirac delta function
distribution-valued potential ⓘ zero-range potential ⓘ |
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: Schrödinger equation with point interactions Description of subject: The Schrödinger equation with point interactions is a quantum-mechanical model in which particles interact via idealized zero-range potentials, typically represented mathematically by Dirac delta functions.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Schrödinger equation with point interactions