Conversely, anti-symmetrization converts any function in n variables into an antisymmetric function.

This χ is the ultimate quantity of interest; it is an antisymmetric function of ω ω.

Traditionally, approximations for the many-body wave function as an antisymmetric function of one-body orbitals have been used, in order to have a manageable treatment of the Schrödinger equation.

For the case of a symmetric diatomic with nuclear spin quantum number I for each nucleus, there are symmetric spin functions and are antisymmetric functions for a total number of nuclear functions .