Generalized coherent states and quantum-classical correspondence

✍ Scribed by Fox, Ronald F.; Choi, Mee Hyang

• Book ID: 118185038
• Publisher: The American Physical Society
• Year: 2000
• Tongue: English
• Weight: 159 KB
• Volume: 61
• Category: Article
• ISSN: 1050-2947
• DOI: 10.1103/physreva.61.032107

✦ Synopsis

Gaussian Klauder coherent states are constructed for the harmonic oscillator, the planar rotor, and the particle in a box. The standard harmonic oscillator coherent states are given by expansions in the eigenstates of the Hamiltonian in terms of a complex parameter ␣. When the complex modulus of ␣ is large, these states are identical in behavior with a particular choice of Gaussian Klauder coherent state. When the angular momentum of a planar rotor is large compared with Planck's constant, the angle distribution associated with a Gaussian Klauder coherent state for this case remains sharply localized for many rotations. Similarly, for the particle in a box, it is possible to choose parameters in the Gaussian Klauder coherent state so that 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 examples show how Gaussian Klauder coherent states are of utility in understanding quantum-classical correspondence.