Time evolution of angular momentum coherent state derived by virtue of entangled state representation and a new binomial theorem

We study how can an angular momentum coherent state |τ> keeps its form-invariant during time evolution governed by the Hamiltonian H=f(t)J₊+f^* (t)J_+ g(t)J_z. We discuss this topic in the context of boson realization of |τ>. By employing the entangled state representation |ζ> and deriving a new binomial theorem involving two-subscript Hermite polynomials, we derive the wave function <ζ|τ>, 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 τ (t) is totally determined by the parameters involved in the Hamiltonian.