On the solutions of the position-dependent effective mass Schrödinger equation of a nonlinear oscillator related with the isotonic oscillator

Abstract

We study exact solutions of the position-dependent effective mass Schrödinger equation by considering the new solvable nonlinear oscillator that relates to the isotonic oscillator through the method of point canonical transformations. We construct exactly solvable potentials by choosing physically important position-dependent mass distributions. We also provide the energy spectrum of the bound states and the wavefunctions of the solvable potentials.