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arXiv · 0707.3624

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

A. Ganguly·L. M. Nieto
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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.

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A. Ganguly, L. M. Nieto. 2007-07-24. Shape-invariant quantum Hamiltonian with position-dependent effective mass through second order supersymmetry. https://doi.org/10.1088/1751-8113/40/26/012

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