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

摘要

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