Coherent states of the two-dimensional non-separable supersymmetric Morse potential

Abstract

Supersymmetry is a fundamental feature of a quantum theory described by a supersymmetric Hamiltonian comprised of several quantum mechanical Hamiltonians with different potentials that allows us to relate information about the states and spectra of the constituent Hamiltonians. In this paper we reconstruct Ioffe's set of states for the singular non-separable two-dimensional Morse potential using supersymmetry from a non-degenerate set of states constructed for the initial separable Morse Hamiltonian. We define generalised coherent states, compute their uncertainty relations, and we find that the singularity in the partner Hamiltonian significantly affects the localisation of the coherent state wavefunction.