Slater determinant

The Slater determinant (after John C. Slater ) is an approximation approach to solving the Schrödinger equation of a system with N identical fermions.

This wave function is an anti- symmetrisiertes product consisting of N orthonormal Einelektronenfunktionen, which are obtained by the Hartree -Fock approach.

Motivation

For a system of N indistinguishable electrons adopted a complete orthonormal system of states is given, expressed by the product wave functions of all possible permutations of the single-particle states. For quantum physics point of view, the particles of a many-body system just are not distinguishable. This means that certain symmetry conditions to be placed on the corresponding wave function: in the case of fermions, it must be antisymmetric to any exchange of two particles. The Slater determinant of single-particle states written - In order to ensure this, is - as shown below.

Herleitungsskizze

Wave function:

The function argument is the atomic number of each electron, for example,. To satisfy the Pauli principle the Antisymmetrisierungsoperator shall be added, namely:

Result

The Slater determinant can be written as follows: