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.

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All labels observed (3)

Label	Occurrences
Slater determinant canonical	2
Slater determinants	1
the Hartree–Fock determinant is a stationary point of the energy	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 ⓘ
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 ⓘ
introducedInField	atomic physics ⓘ quantum chemistry ⓘ
namedAfter	John C. Slater ⓘ
relatedTo	Hartree product ⓘ
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 ⓘ 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

Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

Hartree–Fock method → usesConcept → Slater determinant ⓘ

John C. Slater → knownFor → Slater determinant ⓘ

Brillouin theorem → assumes → the Hartree–Fock determinant is a stationary point of the energy ⓘ

linked to: Slater determinant

Brillouin theorem → relatesTo → Slater determinants ⓘ