Degeneracy and coherent states of the two-dimensional Morse potential

TL;DR

This paper constructs and analyzes coherent states for the two-dimensional Morse potential, exploring how parameter choices influence degeneracies and the properties of these states.

Contribution

It introduces a method to construct coherent states for the 2D Morse potential and studies the impact of physical parameters on degeneracies and state properties.

Findings

Accidental degeneracies depend on parameter irrationality.

Under certain conditions, energy levels are at most two-fold degenerate.

Constructed generalized coherent states and analyzed their probability distributions.

Abstract

In this paper we construct coherent states for the two-dimensional Morse potential. We find the dependence of the spectrum on the physical parameters and use this to understand the emergence of accidental degeneracies. It is observed that, under certain conditions pertaining to the irrationality of the parameters, accidental degeneracies do not appear and as such energy levels are at most two-fold degenerate. After defining a non-degenerate spectrum and set of states for the 2D Morse potential, we construct generalised coherent states and discuss the spatial distribution of their probability densities and their uncertainty relations.