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

Understand

An exactly solvable position-dependent mass Schr\"odinger 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.