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

Abstract

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.

26 pages, no figure, reduced secs. 4 and 5, final version to appear in JPA

References in corpus (18)

• Supersymmetry and Quantum Mechanics
• Effective Mass of One 4he Atom in Liquid 3he
• Solutions of the nonrelativistic wave equation with position-dependent effective mass
• Deformed algebras, position-dependent effective masses and curved spaces: An exactly solvable Coulomb problem
• Exact solvability of potentials with spatially dependent effective masses
• New Eaxactly Solvable Hamiltonians: Shape Invariance and Self-Similarity
• A general scheme for the effective-mass Schrodinger equation and the generation of the associated potentials
• A systematic study on the exact solution of the position dependent mass Schroedinger equation
• Supersymmetric approach to exactly solvable systems with position-dependent effective masses
• Exactly Solvable Potentials and Quantum Algebras
• Exact solutions of effective-mass Schrodinger equations
• New Shape Invariant Potentials in Supersymmetric Quantum Mechanics
• Remarks on supersymmetry of quantum systems with position-dependent effective masses
• Deformed Conformal and Supersymmetric Quantum Mechanics
• Cyclic Shape Invariant Potentials
• Effective-mass Schroedinger equation and generation of solvable potentials
• Application of nonlinear deformation algebra to a physical system with Pöschl-Teller potential
• Exactly solvable models of supersymmetric quantum mechanics and connection to spectrum generating algebra

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