On a classical limit for electronic degrees of freedom that satisfies the Pauli exclusion principle

Fermions need to satisfy the Pauli exclusion principle: no two can be in th e same state. This restriction is most compactly expressed in a second quan tization formalism by the requirement that the creation and annihilation op erators of the electrons satisfy anti-commutation relations. The usual clas sical limit of quantum mechanics corresponds to creation and annihilation o perators that satisfy commutation relations, as for a harmonic oscillator. We discuss a simple classical limit for Fermions. This limit is shown to co rrespond to an anharmonic oscillator, with just one bound excited state. Th e vibrational quantum number of this anharmonic oscillator, which is theref ore limited to the range 0 to 1, is the classical analog of the quantum mec hanical occupancy. This interpretation is also true for Bosons, except that they correspond to a harmonic oscillator so that the occupancy is from 0 u p. The formalism is intended to be useful for simulating the behavior of hi ghly correlated Fermionic systems, so the extension to many electron states is also discussed.