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Supersymmetric approach to exactly solvable systems with position-dependent effective masses

Besire Gonul·Bulent Gonul·Dilek Tutcu·Okan Ozer
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Abstract

We discuss the relationship between exact solvability of the Schrödinger equation with a position-dependent mass and the ordering ambiguity in the Hamiltonian operator within the frame of supersymmetric quantum mechanics. The one-dimensional Schrödinger equation, derived from the general form of the effective mass Hamiltonian, is solved exactly for a system with exponentially changing mass in the presence of a potential with similar behaviour, and the corresponding supersymmetric partner Hamiltonians are related to the effective-mass Hamiltonians proposed in the literature.

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Besire Gonul, Bulent Gonul, Dilek Tutcu, Okan Ozer. 2002-11-20. Supersymmetric approach to exactly solvable systems with position-dependent effective masses. https://doi.org/10.1142/s0217732302008563

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