Abstract
The generalization of the concept of coherent states for a Morse potential based on the real or complex displacements of the equilibrium position of the ground-state wave function yields a natural framework for their generation via Franck-Condon transitions. We study the relevance of including continuum states in the proper treatment of these displaced states, particularly for the description of their time evolution. It is shown that displaced Morse states may exhibit mathematical and physical temporal stability manifested through the presence of revivals in spite of the unbound character of the included continuum states. The Wigner function of these states is presented as well as relations to previous constructions. The time evolution of particular phase space properties such as mean values of position and momentum as well as their uncertainties are also analyzed.
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