Deformed Morse-like potential

TL;DR

This paper introduces a deformed Morse-like potential that is exactly solvable, supports both bound and resonance states, and connects finite and infinite spectrum regimes through a deformation parameter.

Contribution

It presents a new exactly solvable one-dimensional potential generalizing the Morse potential with a deformation that preserves finite spectra.

Findings

Supports bound and resonance states

Transitions from finite to infinite spectrum at zero deformation

Provides explicit energy spectrum and eigenstates

Abstract

We introduce an exactly solvable one-dimensional potential that supports both bound and/or resonance states. This potential is a generalization of the well-known 1D Morse potential where we introduced a deformation that preserves the finite spectrum property. On the other hand, in the limit of zero deformation, the potential reduces to the exponentially confining potential well introduced recently by A. D. Alhaidari. The latter potential supports infinite spectrum which means that the zero deformation limit is a critical point where our system will transition from the finite spectrum limit to the infinite spectrum limit. We solve the corresponding Schrodinger equation and obtain the energy spectrum and the eigenstates using the tridiagonal representation approach.