Generalized coherent states and quantum-classical correspondence - art. no. 032107

Gaussian Klauder coherent states are constructed for the harmonic oscillato r, the planar rotor, and the particle in a box. The standard harmonic oscil lator coherent states are given by expansions in the eigenstates of the Ham iltonian in terms of a complex parameter alpha. When the complex modulus of ct is large, these states are identical in behavior with a particular choi ce of Gaussian Klauder coherent state. When the angular momentum of a plana r rotor is large compared with Planck's constant,the angle distribution ass ociated with a Gaussian Klauder coherent state for this case remains sharpl y localized for many rotations. Similarly, for the particle in a box, it is possible to choose parameters in the Gaussian Klauder coherent state so th at a localized particle bounces back and forth at constant velocity between the walls of the box for many periods without significant delocalization. Buried in this behavior is the Fourier series for a triangle wave. These ex amples show how Gaussian Klauder coherent states are of utility in understa nding quantum-classical correspondence.