Slater determinants

In quantum mechanics, a Slater determinant is an expression that describes the wave function of a multi-fermionic system that satisfies anti-symmetry requirements, and consequently the Pauli principle, by changing sign upon exchange of two electrons (or other fermions). It is named for John C. Slater, who introduced the determinant in 1929 as a means of ensuring the antisymmetry of a wave function, although the wave function in the determinant form first appeared independently in Heisenberg's and Dirac's papers three years earlier. 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, ${\displaystyle \chi (\mathbf {x} )}$, where ${\displaystyle \mathbf {x} }$ 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 which is zero everywhere.

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