New approach to (quasi)-exactly solvable Schrodinger equations with a position-dependent effective mass

Abstract

By using the point canonical transformation approach in a manner distinct from previous ones, we generate some new exactly solvable or quasi-exactly solvable potentials for the one-dimensional Schrödinger equation with a position-dependent effective mass. In the latter case, SUSYQM techniques provide us with some additional new potentials.

11 pages, no figure

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• N-fold Supersymmetry in Quantum Systems with Position-dependent Mass
• Pseudo-Hermiticity and some consequences of a generalized quantum condition
• A generalized quantum nonlinear oscillator
• Quantum solvability of a general ordered position dependent mass system: Mathews-Lakshmanan oscillator
• Morse potential and its relationship with the Coulomb in a position-dependent mass background
• A new effective mass Hamiltonian and associated Lame equation: bound states
• Position Dependent Mass Schroedinger Equation and Isospectral Potentials : Intertwining Operator approach
• Spectrum generating algebras for position-dependent mass oscillator Schrodinger equations
• Spectroscopy of drums and quantum billiards: perturbative and non-perturbative results
• Effect of Position-dependent Mass on Dynamical Breaking of Type B and Type X_2 N-fold Supersymmetry
• Remarks on the Solution of the Position Dependent Mass (PDM) Schrödinger Equation
• Explicit Solutions for N-Dimensional Schrodinger Equations with Position-Dependent 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
• Two-dimensional Schrödinger Hamiltonians with Effective Mass in SUSY Approach
• An extended scenario for the Schrodinger equation
• Equivalence of two alternative approaches to Schrodinger equations
• Novel exactly solvable Schrödinger equations with a position-dependent mass in multidimensional spaces obtained from duality
• CPT-conserved effective mass Hamiltonians through first and higher order charge operator C in a supersymmetric framework
• An alternative approach to Schrödinger equations with a spatially varying mass
• Quantization of Liénard's nonlinear harmonic oscillator and its solutions in the framework of supersymmetric quantum mechanics
• Mapping of Two-Dimensional Schrödinger Equation under the Point Transformation