Space-Time Dynamics of Gazeau-Klauder Coherent States in Power-Law Potentials

Gazeau-Klauder coherent states are developed for power-law potentials and their evolution in space and time is analyzed. We show that these states follow classical dynamics as long as the underlying energy spectrum is linear, otherwise they follow a classical-like evolution upto a few classical periods and disperse thereafter, despite its special construction. Auto-correlation function and probability density as a function of space and time explain the spatio-temporal behavior of these states.