Exact solutions of the Schrödinger equation are obtained for the Rosen–Morse and Scarf potentials with the position-dependent effective mass by appliying a general point canonical transformation. The general form of the point canonical transformation is introduced by using a free parameter. Two 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.
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Tezcan, C., Sever, R. Exact Solutions of the Schrödinger Equation with Position-dependent Effective Mass via General Point Canonical Transformation. J Math Chem 42, 387–395 (2007). https://doi.org/10.1007/s10910-006-9109-6
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DOI: https://doi.org/10.1007/s10910-006-9109-6
Keywords
- position-dependent mass
- point canonical transformation
- effective mass Schrödinger equation
- Rosen–Morse potential
- Scarf potential