A new effective mass Hamiltonian and associated Lame equation: bound states

Abstract

A new quantum model with rational functions for the potential and effective mass is proposed in a stretchable region outside which both are constant. Starting from a generalized effective mass kinetic energy operator the matching and boundary conditions for the envelope wave functions are derived. It is shown that in a mapping to an auxiliary constant-mass Schrodinger picture one obtains one-period ``associated Lame'' well bounded by two delta-wells or delta-barriers depending on the values of one ordering parameter. The results for bound states of this new solvable model are provided for a wide variation of the parameters.

To be published in J.Phys.A (Present e-mail of AG: [email protected])

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Cited by in corpus (20)

• Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
• Position Dependent Mass Oscillators and Coherent States
• Shape-invariant quantum Hamiltonian with position-dependent effective mass through second order supersymmetry
• Position-dependent mass, finite-gap systems, and supersymmetry
• Trends in supersymmetric quantum mechanics
• Nonlinear Dynamics of a position-dependent mass driven Duffing-type oscillator
• Hidden nonlinear su(2|2) superunitary symmetry of N=2 superextended 1D Dirac delta potential problem
• Spectrum generating algebras for position-dependent mass oscillator Schrodinger equations
• Quantization of Hamiltonian systems with a position dependent mass: Killing vector fields and Noether momenta approach
• Remarks on the Solution of the Position Dependent Mass (PDM) Schrödinger Equation
• Coherent and squeezed states: introductory review of basic notions, properties and generalizations
• Peculiarities of the hidden nonlinear supersymmetry of Poschl-Teller system in the light of Lame equation
• Schroedinger equations with indefinite effective mass
• Oscillator-Morse-Coulomb mappings and algebras for constant or position-dependent mass
• Nonsingular potentials from excited state factorization of a quantum system with position dependent mass
• A quasi-free position-dependent-mass jump and self-scattering correspondence
• Supersymmetry Across Nanoscale Heterojunction
• CPT-conserved effective mass Hamiltonians through first and higher order charge operator C in a supersymmetric framework
• Supersymmetric partners for the associated Lame potentials
• Mapping of Two-Dimensional Schrödinger Equation under the Point Transformation