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

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]

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• Position Dependent Mass Schroedinger Equation and Isospectral Potentials : Intertwining Operator approach
• Quantization of Hamiltonian systems with a position dependent mass: Killing vector fields and Noether momenta approach
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• Supersymmetric Analysis of the Dirac-Weyl Operator within PT Symmetry
• Supersymmetry Across Nanoscale Heterojunction
• Nonlinear supersymmetry as a hidden symmetry
• Applications of the potential algebras of the two-dimensional Dirac-like operators
• A complete set of eigenstates for position-dependent massive particles in a Morse-like scenario
• Supersymmetric Partners of the One-Dimensional Infinite Square Well Hamiltonian
• CPT-conserved effective mass Hamiltonians through first and higher order charge operator C in a supersymmetric framework
• Mapping of Two-Dimensional Schrödinger Equation under the Point Transformation
• Comparison theorems for the position-dependent mass Schroedinger equation
• 2N-Dimensional Canonical Systems and Applications