Slater determinant
E645110
antisymmetric wavefunction
fermionic wavefunction
many-electron wavefunction
mathematical object in quantum mechanics
tool in atomic physics
tool in quantum chemistry
A Slater determinant is an antisymmetrized many-electron wavefunction constructed from single-particle orbitals that enforces the Pauli exclusion principle in quantum chemistry and atomic physics.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Slater determinant canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7150535 — 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: Slater determinant Context triple: [Hartree–Fock method, usesConcept, Slater determinant]
-
A.
Hartree–Fock method
The Hartree–Fock method is an approximate quantum mechanical approach for determining the electronic structure of atoms, molecules, and solids by modeling electrons as occupying self-consistent single-particle orbitals.
-
B.
Clebsch–Gordan coefficients
Clebsch–Gordan coefficients are numerical factors in quantum mechanics and representation theory that describe how to combine two angular momenta (or group representations) into a single resultant one.
-
C.
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.
-
D.
Schmidt decomposition
The Schmidt decomposition is a mathematical technique in functional analysis and quantum information theory that expresses a bipartite vector (such as a quantum state) as a sum of orthogonal product states with nonnegative coefficients, revealing its entanglement structure.
-
E.
Born–Huang expansion
The Born–Huang expansion is a quantum mechanical method that systematically improves upon the Born–Oppenheimer approximation by including couplings between electronic and nuclear motions in molecular systems.
- 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: Slater determinant Target entity description: A Slater determinant is an antisymmetrized many-electron wavefunction constructed from single-particle orbitals that enforces the Pauli exclusion principle in quantum chemistry and atomic physics.
-
A.
Hartree–Fock method
The Hartree–Fock method is an approximate quantum mechanical approach for determining the electronic structure of atoms, molecules, and solids by modeling electrons as occupying self-consistent single-particle orbitals.
-
B.
Clebsch–Gordan coefficients
Clebsch–Gordan coefficients are numerical factors in quantum mechanics and representation theory that describe how to combine two angular momenta (or group representations) into a single resultant one.
-
C.
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.
-
D.
Schmidt decomposition
The Schmidt decomposition is a mathematical technique in functional analysis and quantum information theory that expresses a bipartite vector (such as a quantum state) as a sum of orthogonal product states with nonnegative coefficients, revealing its entanglement structure.
-
E.
Born–Huang expansion
The Born–Huang expansion is a quantum mechanical method that systematically improves upon the Born–Oppenheimer approximation by including couplings between electronic and nuclear motions in molecular systems.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
antisymmetric wavefunction
ⓘ
fermionic wavefunction ⓘ many-electron wavefunction ⓘ mathematical object in quantum mechanics ⓘ tool in atomic physics ⓘ tool in quantum chemistry ⓘ |
| appliesTo |
many-electron atoms
ⓘ
molecules ⓘ solids in independent-electron approximations ⓘ systems of identical fermions ⓘ |
| assumes | electrons move independently in an effective mean field ⓘ |
| basisFor |
multi-determinant wavefunction expansions
ⓘ
single-determinant Hartree–Fock approximation ⓘ |
| belongsTo | fermionic Fock space ⓘ |
| constructedFrom |
one-electron orbitals
ⓘ
single-particle spin-orbitals ⓘ |
| differsFrom | Hartree product by antisymmetrization ⓘ |
| enforces | Pauli exclusion principle NERFINISHED ⓘ |
| ensures |
orthogonality of states built from orthonormal orbitals
ⓘ
proper antisymmetry of fermionic wavefunction ⓘ |
| generalizes | two-electron antisymmetric singlet wavefunction ⓘ |
| hasComponent |
spatial orbitals
ⓘ
spin degrees of freedom ⓘ |
| hasMathematicalForm |
1/sqrt(N!) times determinant of orbital matrix for N electrons
ⓘ
determinant of a matrix of spin-orbitals evaluated at electron coordinates ⓘ |
| hasProperty |
antisymmetric under exchange of any two electrons
ⓘ
changes sign under particle exchange ⓘ vanishes when two electrons occupy the same spin-orbital ⓘ |
| introducedBy | John C. Slater NERFINISHED ⓘ |
| introducedInField |
atomic physics
ⓘ
quantum chemistry ⓘ |
| namedAfter | John C. Slater NERFINISHED ⓘ |
| relatedTo | Hartree product NERFINISHED ⓘ |
| represents |
approximate ground-state wavefunction
ⓘ
excited-state wavefunction ⓘ fermionic Fock state in first quantization ⓘ independent-particle model of electrons ⓘ |
| usedAs |
basis function in configuration interaction expansions
ⓘ
reference state in Hartree–Fock theory ⓘ trial wavefunction in quantum Monte Carlo ⓘ trial wavefunction in variational calculations ⓘ |
| usedIn |
Hartree–Fock method
NERFINISHED
ⓘ
configuration interaction ⓘ molecular electronic structure theory ⓘ multi-configurational self-consistent field ⓘ n-electron atomic structure calculations ⓘ nuclear shell model ⓘ quantum Monte Carlo methods ⓘ second quantization formalism ⓘ |
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: Slater determinant Description of subject: A Slater determinant is an antisymmetrized many-electron wavefunction constructed from single-particle orbitals that enforces the Pauli exclusion principle in quantum chemistry and atomic physics.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.