A systematic study on the exact solution of the position dependent mass Schroedinger equation

Abstract

An algebraic method of constructing potentials for which the Schroedinger equation with position dependent mass can be solved exactly is presented. A general form of the generators of su(1,1) algebra has been employed with a unified approach to the problem. Our systematic approach reproduces a number of earlier results and also leads to some novelties. We show that the solutions of the Schroedinger equation with position dependent mass are free from the choice of parameters for position dependent mass. Two classes of potentials are constructed that include almost all exactly solvable potentials.

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• Superintegrable systems with position dependent mass
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• A Quantum Quasi-Harmonic Nonlinear Oscillator with an Isotonic Term
• Spectrum generating algebras for position-dependent mass oscillator Schrodinger equations
• Analytical Solutions of Klein-Gordon Equation with Position-Dependent Mass for q-Parameter Poschl-Teller potential
• Spectroscopy of drums and quantum billiards: perturbative and non-perturbative results
• Pseudo-Hermitian versus Hermitian position-dependent-mass Hamiltonians in a perturbative framework
• Coherent state of a nonlinear oscillator and its revival dynamics
• Remarks on the Solution of the Position Dependent Mass (PDM) Schrödinger Equation
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