Time evolution of linear and generalized Heisenberg algebra nonlinear Pöschl-Teller coherent states

Abstract

We analyze the time evolution of two kinds of coherent states for a particle in a P\"oschl-Teller potential. We find a pair of canonically conjugate operators and compare the behavior of their time evolution for both coherent states. The nonlinear ones are more localized. The trajectory in the phase space of the mean values of these two operators is a kind of generalization of the Rose algebraic curves. The new pair of canonically conjugate variables leads to a fourth-order Schr\"odinger equation which has the same energy spectrum as the P\"oschl-Teller system.