Intermediate-statistics quantum bracket, coherent state, oscillator, and representation of angular momentum [su(2)] algebra

摘要

In this paper, we first discuss the general properties of an intermediate-statistics quantum bracket, [u,upsilon](n)=u upsilon-e(i2 pi/(n+1))upsilon u, which corresponds to intermediate statistics in which the maximum occupation number of one quantum state is an arbitrary integer, n. A further study of the operator realization of intermediate statistics is given. We construct the intermediate-statistics coherent state. An intermediate-statistics oscillator is constructed, which returns to bosonic and fermionic oscillators respectively when n ->infinity and n=1. The energy spectrum of such an intermediate-statistics oscillator is calculated. Finally, we discuss the intermediate-statistics representation of angular momentum [su(2)] algebra. Moreover, a further study of the operator realization of intermediate statistics is given in the Appendix.