Allowed permutation symmetry in atomic and molecular wavefunctions: simple examples

Abstract

It is well known that the allowed wavefunctions for an N-electron system should be antisymmetric with respect to the permutation of any pair of electron labels. On the other hand, the Hamiltonian for such a system is invariant under any permutation of electron labels and, consequently, its eigenfunctions are the basis for the irreducible representations of the symmetric group S N. Here, we investigate which symmetry species of the S N group are compatible with the antisymmetry principle. We illustrate the conclusions by means of simple N-particle one-dimensional models with harmonic interactions.