Semiclassical approximations in the coherent-state representation

We analyze the semiclassical limit of the stationary Schrödinger equation in the coherent-state representation simultaneously for the groups $W_1$, SU(2), and SU(1,1). A simple expression for the first two orders for the wave function and the associated semiclassical quantization rule is obtained if a definite choice for the classical Hamiltonian and expansion parameter is made. The behavior of the modulus of the wave function, which is a distribution function in a curved phase space, is studied for the three groups. The results are applied to the quantum triaxial rotor.