Exact solutions of the Schrödinger equation with position-dependent mass for some Hermitian and non-Hermitian potentials

Abstract

We study the exact solutions of the Schrödinger equation with position-dependent mass by using the method of point canonical transformations. Given a position-dependent mass distribution, we construct the exactly solvable target potentials by choosing the Rosen–Morse-type and Scarf-type potentials as the reference potentials. The energy spectra of the bound states and corresponding wavefunctions for the target potentials are given explicitly.