We use the method of point canonical transformations and choose the Rosen-Morse-type potential as the reference potential to study exact solutions of the position-dependent effective mass Schrödinger equations. Choosing three position-dependent mass distributions, we construct seven exactly solvable target potentials with PT symmetry. The energy spectra of the bound states and corresponding wavefunctions for the PT-symmetric potentials are given in the exact closed forms. We also discuss the isospectrality of different Schrödinger equations with the same mass distribution or different mass distributions for different PT-symmetric potentials.
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Jia, CS., Yi, LZ. & Sun, Y. Position-dependent effective mass Schrödinger equations for PT-symmetric potentials. J Math Chem 43, 435–446 (2008). https://doi.org/10.1007/s10910-006-9206-6
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DOI: https://doi.org/10.1007/s10910-006-9206-6