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Quadratic Algebra Approach to an Exactly Solvable Position-Dependent Mass Schr dinger Equation in Two Dimensions

Keywords: Schr dinger equation , position-dependent mass , quadratic algebra

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Abstract:

An exactly solvable position-dependent mass Schr dinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems with integrals of motion that are quadratic functions of the momenta. To get the energy spectrum a quadratic algebra approach is used together with a realization in terms of deformed parafermionic oscillator operators. In this process, the importance of supplementing algebraic considerations with a proper treatment of boundary conditions for selecting physical wavefunctions is stressed. Some new results for matrix elements are derived. This example emphasizes the interest of a quadratic algebra approach to position-dependent mass Schr dinger equations.

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