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Hamiltonians with position-dependent mass, deformations and supersymmetry

C. Quesne·B. Bagchi·A. Banerjee·V. M. Tkachuk
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Abstract

A new method for generating exactly solvable Schrödinger equations with a position-dependent mass is proposed. It is based on a relation with some deformed Schrödinger equations, which can be dealt with by using a supersymmetric quantum mechanical approach combined with a deformed shape-invariance condition. The solvability of the latter is shown to impose the form of both the deformed superpotential and the position-dependent mass. The conditions for the existence of bound states are determined. A lot of examples are provided and the corresponding bound-state spectrum and wavefunctions are reviewed.

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C. Quesne, B. Bagchi, A. Banerjee, V. M. Tkachuk. 2005-12-06. Hamiltonians with position-dependent mass, deformations and supersymmetry. https://arxiv.org/abs/quant-ph/0512046

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