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Quadratic algebra approach to an exactly solvable position-dependent mass Schrödinger equation in two dimensions

par Quesne, Christiane
Référence Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 3, 067
Publication Publié, 2007

Article révisé par les pairs

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Résumé :

An exactly solvable position-dependent mass Schrödinger 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 Schrödinger equations.