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

• Main Author: Christiane Quesne
• Format: Article
• Language: English
• Published: National Academy of Science of Ukraine 2007-05-01
• Series: Symmetry, Integrability and Geometry: Methods and Applications
• Subjects: Schrödinger equation; position-dependent mass; quadratic algebra
• Online Access: http://www.emis.de/journals/SIGMA/2007/067/

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.