SUSY-Nonrelativistic Quantum Eigenspectral Energy Analysis for Squared-Type Trigonometric Potentials Through Nikiforov-Uvarov Formalism

TL;DR

This paper derives explicit bound-state solutions for squared trigonometric potentials in supersymmetric quantum mechanics using the Nikiforov-Uvarov method, providing analytical energy spectra and wave functions applicable to various quantum systems.

Contribution

It introduces a novel application of the Nikiforov-Uvarov formalism to SUSYQM for squared trigonometric potentials, yielding analytical solutions and energy spectra.

Findings

Analytical bound-state solutions for the potentials obtained.

Normalized wave functions derived explicitly.

Energy spectra characterized algebraically.

Abstract

Explicit and analytical bound-state solutions of the Schrodinger equation for squared-form trigonometric potentials within the framework of supersymmetric quantum mechanics (SUSYQM) are performed by implementing the Nikiforov-Uvarov (NU) polynomial procedure. The first step requires a certain action to adopt an appropriate ansatz superpotential W(x) for generating the potential pair as V1 (x) and V2(x). In the second process, inserting each potential for the one-dimensional Schrodinger equation and solving the hypergeometric differential equation with the NU method gives rise to normalized wave function descriptions and algebraically corresponds to the characteristic SUSY quantum energy eigenspectrum sets. It is remarkable to note that, when examined parametrically, they are of reliable and applicable forms concerning the mathematical treatment of various physical quantum systems prescribed in relativistic or nonrelativistic contexts.