Shape-invariant quantum Hamiltonian with position-dependent effective mass through second order supersymmetry
arXiv:0707.3624 · doi:10.1088/1751-8113/40/26/012
Abstract
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.
16 pages, 5 figs; Present e-mail of AG: [email protected]