Temporally stable coherent states for infinite well and Pöschl–Teller potentials

Abstract

This article is a direct illustration of a construction of coherent states which has been recently proposed by two of us (JPG and JK). We have chosen the example of a particle trapped in an infinite square-well and also in Pöschl–Teller potentials of the trigonometric type. In the construction of the corresponding coherent states, we take advantage of the simplicity of the solutions, which ultimately stems from the fact they share a common SU(1,1) symmetry à la Barut-Girardello. Many properties of these states are then studied, both from mathematical and from physical points of view.