Higher order SUSY-QM for P\"oschl-Teller potentials: coherent states and operator properties

TL;DR

This paper extends previous work on supersymmetric quantum mechanics for P"oschl-Teller potentials by explicitly computing eigenfunctions, spectra, and analyzing properties of higher order coherent states and operator forms.

Contribution

It provides explicit eigenfunction and spectrum calculations for higher order SUSY-QM Hamiltonians and analyzes their properties and coherent states.

Findings

Explicit eigenfunctions and spectra for higher order SUSY-QM Hamiltonians.

Analysis of normal and anti-normal forms of operators.

Characterization of coherent states for P"oschl-Teller potentials.

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 P\"oschl-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 $A_{m,\nu,\beta}$ of the P\"oschl-Teller Hamiltonian $H_{\nu,\beta}^{(m)}$ and their characteristics are studied.