Trajectories of generalized quantum states for systems with finite discrete spectrum and classical analogs

In this paper, we construct generalized quantum states for systems with finite discrete spectrum and compare the behavior of those states with the classical analogs. Phase-space trajectories are analyzed in the classical and quantum cases. We focus on the following bounded anharmonic exactly solvable one-dimensional potentials: Morse, hyperbolic Poschl-Teller and Rosen-Morse.