  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. This example emphasizes the interest of a quadratic algebra approach
to position-dependent mass Schr\"odinger equations.
