Deformed shape invariance and exactly solvable Hamiltonians with position-dependent effective mass

By B. Bagchi, A. Banerjee, Christiane Quesne, V. Tkachuk. 2004

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Known shape-invariant potentials for the constant-mass Schrodinger equation are taken as effective potentials in a position-dependent effective mass (PDEM) one. The corresponding shape-invariance condition turns out to be deformed. Its solvability imposes the form of both the deformed superpotential and the PDEM. A lot of new exactly solvable potentials associated with a PDEM background are generated in this way. A novel and important condition restricting the existence of bound states whenever the PDEM vanishes at an end point of the interval is identified. In some cases, the bound-state spectrum results from a smooth deformation of that of the conventional shape-invariant potential used in the construction. In others, one observes a generation or suppression of bound states, depending on the mass-parameter values. The corresponding wavefunctions are given in terms of some deformed classical orthogonal polynomials.

Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e4a4473138eaf6b3811fb69fb60d8a1c6ba2c6aa