Temporally stable coherent states for infinite well and P\"oschl-Teller potentials

TL;DR

This paper constructs and analyzes temporally stable coherent states for particles in infinite well and P"oschl-Teller potentials, leveraging SU(1,1) symmetry to explore their properties.

Contribution

It introduces a method for constructing coherent states for specific quantum potentials using SU(1,1) symmetry, demonstrating their stability and properties.

Findings

Coherent states exhibit temporal stability.

States possess SU(1,1) symmetry.

Mathematical and physical properties are analyzed.

Abstract

This paper 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 P\"oschl-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 \`a la Barut--Girardello. Many properties of these states are then studied, both from mathematical and from physical points of view.