Gazeau-Klauder coherent states for a one-mode system with sinusoidal potent
ial, are introduced. Their quantum statistical properties and their uncerta
inties are studied. The effect of dissipation on these states is estimated.
The evolution of the ordinary (Glauber) coherent states in this system, is
also studied. It is shown that these states evolve into superpositions of
many macroscopically distinguishable states ('multi-Schrodinger cats').