Editing Slater determinant (section)

{{short description|Function that can be used to build the wave function of a multi-fermionic system}}
In [[quantum mechanics]], a '''Slater determinant'''  is an expression that describes the [[wave function]] of a multi-[[fermion]]ic system. It satisfies [[Skew-symmetric matrix|anti-symmetry]] requirements, and consequently the [[Pauli principle]], by changing [[Plus and minus signs|sign]] upon exchange of two fermions.<ref name="Atkins">Molecular Quantum Mechanics Parts I and II: An Introduction to QUANTUM CHEMISTRY (Volume 1), P. W. Atkins, Oxford University Press, 1977, {{ISBN|0-19-855129-0}}.</ref> Only a small subset of all possible many-body fermionic wave functions can be written as a single Slater determinant, but those form an important and useful subset because of their simplicity.

The Slater determinant arises from the consideration of a wave function for a collection of electrons, each with a wave function known as the [[spin-orbital]] <math>\chi(\mathbf{x})</math>, where <math>\mathbf{x}</math> denotes the position and spin of a single electron. A Slater determinant containing two electrons with the same spin orbital would correspond to a wave function that is zero everywhere.

The Slater determinant is named for [[John C. Slater]], who introduced the determinant in 1929 as a means of ensuring the antisymmetry of a many-electron wave function,<ref>{{cite journal |last1=Slater |first1=J. |title=The Theory of Complex Spectra |journal=Physical Review |volume=34 |issue=2 |pages=1293–1322 |year=1929  |doi=10.1103/PhysRev.34.1293 |bibcode = 1929PhRv...34.1293S }}</ref> although the wave function in the determinant form first appeared independently in Heisenberg's<ref>{{cite journal |last1 = Heisenberg |first1 = W. |title = Mehrkörperproblem und Resonanz in der Quantenmechanik |journal = Zeitschrift für Physik |year = 1926 |volume = 38 |issue = 6–7 |pages = 411–426 |doi= 10.1007/BF01397160 |bibcode = 1926ZPhy...38..411H |s2cid = 186238286 }}</ref> and Dirac's<ref>{{cite journal |last1 = Dirac |first1 = P. A. M. |title = On the Theory of Quantum Mechanics |journal = Proceedings of the Royal Society A |year = 1926 |volume = 112 |issue = 762 |pages = 661–677 |doi= 10.1098/rspa.1926.0133 |bibcode = 1926RSPSA.112..661D |doi-access = free }}</ref><ref>{{Cite web |title=Slater determinant in nLab |url=https://ncatlab.org/nlab/show/Slater+determinant#references |access-date=2023-11-08 |website=ncatlab.org}}</ref> articles three years earlier.