Spectrum generating algebras for position-dependent mass oscillator Schrodinger equations

The interest of quadratic algebras for position-dependent mass Schrodinger equations is highlighted by constructing spectrum generating algebras for a class of d-dimensional radial harmonic oscillators with d >= 2 and a specific mass choice depending on some positive parameter a. Via some minor changes, the one-dimensional oscillator on the line with the same kind of mass is included in this class. The existence of a single unitary irreducible representation belonging to the positive-discrete series type for d >= 2 and of two of them for d = 1 is proved. The transition to the constant-mass limit alpha -> 0 is studied and deformed su(1,1) generators are constructed. These operators are finally used to generate all the bound-state wavefunctions by an algebraic procedure.