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])

References in corpus (2)

• Quantum particles trapped in a position-dependent mass barrier; a d-dimensional recipe
• New supersymmetric partners for the associated Lame potentials

Cited by in corpus (6)

• Position Dependent Mass Oscillators and Coherent States
• Shape-invariant quantum Hamiltonian with position-dependent effective mass through second order supersymmetry
• 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
• Peculiarities of the hidden nonlinear supersymmetry of Poschl-Teller system in the light of Lame equation
• Oscillator-Morse-Coulomb mappings and algebras for constant or position-dependent mass