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Deformed shape invariance and exactly solvable Hamiltonians with position-dependent effective mass
B BAGCHI, A BANERJEE, C QUESNE, V M TKACHUK
Published in IOP PUBLISHING LTD
2005
Volume: 38
   
Issue: 13
Pages: 2929 - 2945
Abstract
Known shape-invariant potentials for the constant-mass Schrödinger 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. © 2005 IOP Publishing Ltd.
About the journal
JournalData powered by TypesetJournal of Physics A: Mathematical and General
PublisherData powered by TypesetIOP PUBLISHING LTD
ISSN0305-4470
Open AccessYes