Bulg. J. Phys. vol.33 no.4 (2006), pp. 308-318

Hamiltonians with Position-Dependent Mass, Deformations and Supersymmetry

C. Quesne1, B. Bagchi2, A. Banerjee2, V.M. Tkachuk3
1Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050 Brussels, Belgium
2Department of Applied Mathematics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700 009, India
3Ivan Franko Lviv National University, Chair of Theoretical Physics, 12 Drahomanov Street, Lviv UA-79005, Ukraine
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 wave functions are reviewed.

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