PT-symmetric Solutions of Schrodinger Equation with position-dependent mass via Point Canonical Transformation

TL;DR

This paper derives PT-symmetric solutions for the Schrödinger equation with position-dependent mass using point canonical transformation, exploring different mass distributions and their impact on energy eigenvalues and wave functions.

Contribution

It introduces a general point canonical transformation approach with a free parameter to solve PT-symmetric Schrödinger equations with position-dependent mass.

Findings

Energy eigenvalues depend on the free parameter.

Wave functions are explicitly obtained for different mass distributions.

The method applies to Scarf and generalized harmonic oscillator potentials.

Abstract

PT-symmetric solutions of Schrodinger equation are obtained for the Scarf and generalized harmonic oscillator potentials with the position-dependent mass. A general point canonical transformation is applied by using a free parameter. Three different forms of mass distributions are used. A set of the energy eigenvalues of the bound states and corresponding wave functions for target potentials are obtained as a function of the free parameter.