Levine R D
Fritz Haber Research Center for Molecular Dynamics, Hebrew University, Jerusalem 91904, Israel.
Proc Natl Acad Sci U S A. 2000 Feb 29;97(5):1965-9. doi: 10.1073/pnas.97.5.1965.
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.
两个费米子不能处于同一状态。在二次量子化形式体系中，这一限制最简洁地表述为电子的产生算符和湮灭算符需满足反对易关系。量子力学通常的经典极限对应于满足对易关系的产生算符和湮灭算符，就像对于一个谐振子那样。我们讨论一种费米子的简单经典极限。结果表明，这个极限对应于一个非谐振子，且只有一个束缚激发态。这个非谐振子的振动量子数因此被限制在0到1的范围内，它是量子力学占据数的经典类似物。对于玻色子，这种解释同样成立，只是它们对应于一个谐振子，所以占据数从0开始向上取值。该形式体系旨在用于模拟高度关联的费米子系统的行为，因此也讨论了向多电子态的扩展。
