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This paper is a direct illustration of a construction of coherent stateswhich has been recently proposed by two of us (JPG and JK). We have chosen theexample of a particle trapped in an infinite square-well and also inP\"oschl-Teller potentials of the trigonometric type. In the construction ofthe corresponding coherent states, we take advantage of the simplicity of thesolutions, which ultimately stems from the fact they share a common SU(1,1)symmetry \`a la Barut--Girardello. Many properties of these states are thenstudied, both from mathematical and from physical points of view.Comment: 48 pages, 21 figure

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