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

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.