Slater determinant

In quantum mechanics, a Slater determinant is an expression that describes the wavefunction 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 determinants in 1929 as a means of ensuring the antisymmetry of a wave function. But actually the wave function in the determinant form first appeared three years earlier independently in Heisenberg's and Dirac's papers. 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, , where denotes the position and spin of the singular electron. Two electrons within the same spin orbital result in no wave function.

Resolution

Two-particle case

The simplest way to approximate the wave function of a many-particle system is to take the product of properly chosen orthogonal wave functions of the individual particles. For the two-particle case with spatial coordinates and , we have