Higher order SUSY-QM for Pöschl-Teller potentials: coherent states and operator properties

Abstract

This work prolongs recent investigations by Bergeron et al [see 2012 J. Phys. A: Math. Theo. 45 244028] on new SUSYQM coherent states for Pöschl-Teller potentials. It mainly addresses explicit computations of eigenfunctions and spectrum associated to the higher order hierarchic supersymmetric Hamiltonian. Analysis of relevant properties and normal and anti-normal forms is performed and discussed. Coherent states of the hierarchic first order differential operator $A_{m,ν,β}$ of the Pöschl-Teller Hamiltonian $H_{ν,β}^{(m)}$ and their characteristics are studied.