%0 Journal Article
%T Quadratic Algebra Approach to an Exactly Solvable Position-Dependent Mass Schr dinger Equation in Two Dimensions
%A Christiane Quesne
%J Symmetry, Integrability and Geometry : Methods and Applications
%D 2007
%I National Academy of Science of Ukraine
%X 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.
%K Schr dinger equation
%K position-dependent mass
%K quadratic algebra
%U http://www.emis.de/journals/SIGMA/2007/067/