Exact solution of Schr\"odinger equation with q-deformed quantum potentials using Nikiforov-Uvarov method

TL;DR

This paper derives exact solutions for the one-dimensional Schr"odinger equation with a complex potential combining Wood-Saxon, Rosen-Morse, and double well features using the Nikiforov-Uvarov method, analyzing eigenvalues, eigenfunctions, and symmetry properties.

Contribution

It provides the first exact analytical solutions for this combined potential using the Nikiforov-Uvarov method, including energy spectra and wave functions.

Findings

Eigenvalues and eigenfunctions obtained explicitly

PT-symmetry and Hermiticity analyzed

Special cases discussed with simplified energy equations

Abstract

In this paper, we present the exact solution of one dimensional Schr\"odinger equation for Wood-Saxon plus Rosen-Morse plus symmetrical double well potential via Nikiforov-Uvarov mathematical method. The eigenvalues and eigenfunctions of this potential are obtained. The energy equations and the corresponding wave function for special cases of this potential are briefly discussed. The PT-symmetry and Hermiticity for this potential are also considered.