标题： 中间统计量子括号，相干态，振子以及角动量（su(2））代数的表示 显示英文标题

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

摘要： 本文首先讨论了中间统计量子泊松括号$[ u,v]_{n}=uv-e^{i2\pi /(n+1)}vu$的一般性质，它对应于一种中间统计，其中一个量子态的最大占据数是任意整数$n$。给出了中间统计算符实现的进一步研究。 我们构造了中间统计相干态。 构建了一个中间统计振子，当$n\to \infty $和$n=1$时分别退化为玻色和费米振子。 计算了这种中间统计振子的能量谱。 最后，讨论了角动量（$su(2)$）代数的中间统计表示。 此外，附录中给出了中间统计算符实现的进一步研究。 显示英文摘要

摘要： In this paper, we first discuss the general properties of an intermediate-statistics quantum bracket, $[ u,v]_{n}=uv-e^{i2\pi /(n+1)}vu$, 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\to \infty $ 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.