Open AccessOn a classical limit for electronic degrees of freedom that satisfies the Pauli exclusion principle
Author(s) -
R. D. Levine
Publication year - 2000
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.97.5.1965
Subject(s) - pauli exclusion principle , creation and annihilation operators , anharmonicity , physics , quantum mechanics , fermion , quantization (signal processing) , harmonic oscillator , boson , hamiltonian (control theory) , classical limit , coherent states , quantum , quantum limit , second quantization , quantum number , quantum harmonic oscillator , fock state , mathematics , mathematical optimization , algorithm
Fermions need to satisfy the Pauli exclusion principle: no two can be in the same state. This restriction is most compactly expressed in a second quantization formalism by the requirement that the creation and annihilation operators of the electrons satisfy anticommutation relations. The usual classical limit of quantum mechanics corresponds to creation and annihilation operators that satisfy commutation relations, as for a harmonic oscillator. We discuss a simple classical limit for Fermions. This limit is shown to correspond to an anharmonic oscillator, with just one bound excited state. The vibrational quantum number of this anharmonic oscillator, which is therefore limited to the range 0 to 1, is the classical analog of the quantum mechanical occupancy. This interpretation is also true for Bosons, except that they correspond to a harmonic oscillator so that the occupancy is from 0 up. The formalism is intended to be useful for simulating the behavior of highly correlated Fermionic systems, so the extension to many electron states is also discussed.