Time evolution of angular momentum coherent state derived by virtue of entangled state representation and a new binomial theorem**Project supported by the National Natural Science Foundation of China (Grant No. 11347026) and the Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2016AM03 and ZR2017MA011).

Abstract

We study how can an angular momentum coherent state keeps its form-invariant during time evolution governed by the Hamiltonian . We discuss this topic in the context of boson realization of . By employing the entangled state representation and deriving a new binomial theorem involving two-subscript Hermite polynomials, we derive the wave function , which turns out to be a single-subscript Hermite polynomial. Based on this result the maintenance of angular momentum coherent state during time evolution is examined, and the value of is totally determined by the parameters involved in the Hamiltonian.