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

TL;DR

This paper uses supersymmetry to construct and analyze coherent states for a complex two-dimensional Morse potential, revealing how singularities influence state localization.

Contribution

It reconstructs supersymmetric coherent states for a non-separable Morse potential, extending previous methods to non-trivial, singular quantum systems.

Findings

Singularity impacts the localization of coherent states.

Constructed generalized coherent states for a non-separable Morse potential.

Analyzed uncertainty relations of the coherent states.

Abstract

Supersymmetry is a technique that allows us to extract information about the states and spectra of quantum mechanical systems which may otherwise be unsolvable. 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.