Nonrelativistic and Nonstationary Effective Mass Bound-Spectra Analysis of Squared Class Trigonometric Potentials Through the Point Canonical Formalism

TL;DR

This paper derives exact solutions for the position-dependent effective mass Schrödinger equation with squared trigonometric potentials using the point canonical transformation method, revealing explicit energy spectra and wavefunctions.

Contribution

It introduces a systematic algebraic approach to solve PDEM Schrödinger equations with complex potentials, providing explicit spectral and wavefunction solutions.

Findings

Exact analytical energy spectra obtained for specific potentials

Wavefunctions explicitly derived for the system

Canonical transformations relate original and transformed potentials

Abstract

The present paper engages in a particular attempt to acquire exact analytical eigensolutions of the position-dependent effective mass (PDEM) Schr\"odinger equation for a variety of squared style trigonometric potentials. The algebraic process entitled as the point canonical transformation (PCT) approach is implemented in the course of study. Certain spatially varying effective mass configurations have been utilized in establishing of the target system. Then, performing the systematic computational procedures enables us to determine not only the possible explicit forms of both discrete energy spectra and their corresponding wavefunctions but also canonical counterparts of original potentials, involved in the framework of PDEM based quantum systems.