Temporally stable coherent states for infinite well and Poschl-Teller potentials

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 Po schl-Teller potentials of the trigonometric type. In the construction of th e 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 a la Barut-Girardello. Many properties of these states are then studied, both from mathematical and from physical points of view. (C) 2001 American Institute of Physics.