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

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 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) symmetryà la Barut-Girardello. Many properties of these states are then studied, both from mathematical and from physical points of view.

Sub-Planck-scale structures in the Pöschl-Teller potential and their sensitivity to perturbations

“…The corresponding Schrödinger equation can be solved to obtain the energy eigenvalues and eigenfunctions [24] …”

Generalized coherent states for oscillators connected with Meixner and Meixner—Pollaczek polynomials

“…It is known [12] - [15] that for this purpose we have to solve the Stieltjes classical moment problem [55,56] …”

Coherent States with Complex Functions

“…Recently another class of CS were introduced, by Gazeau and Klauder, for Hamiltonians with discrete and continuous spectrum by taking Φ m (z) = ( √ J) m e iemα and ρ(m) = e 1 e 2 ...e m , where e m 's are the spectrum of the Hamiltonian arranged in a particular way, for details see [7]. Following thir work the same class of CS were studied for various Hamiltonians, for example see [2].…”