Shape-invariant quantum Hamiltonian with position-dependent effective mass through second order supersymmetry

Details Shape-invariant quantum Hamiltonian with position-dependent effective mass through second order supersymmetry Shape-invariant quantum Hamiltonian with position-dependent effective mass through second order supersymmetry

2007-07-24

arxiv.org/abs/0707.3624v1

J.Phys.A40:7265-7281,2007

Physics

Quantum Physics

16 pages, 5 figs; Present e-mail of AG: gangulyasish@rediffmail.com

Scientific paper

10.1088/1751-8113/40/26/012

Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner Hamiltonians may be exploited to obtain a simple shape-invariant condition. Indeed a novel relation between potential and mass functions is derived, which leads to a class of exactly solvable model. As an illustration of our procedure, two examples are given for which one obtains whole spectra algebraically. Both shape-invariant potentials exhibit harmonic-oscillator-like or singular-oscillator-like spectra depending on the values of the shape-invariant parameter.

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