Spectrum generating algebras for position-dependent mass oscillator Schrodinger equations

Abstract

The interest of quadratic algebras for position-dependent mass Schrödinger equations is highlighted by constructing spectrum generating algebras for a class of d-dimensional radial harmonic oscillators with $d\ge 2$ and a specific mass choice depending on some positive parameter $\alpha$. 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 $d\ge 2$ and of two of them for d=1 is proved. The transition to the constant-mass limit $\alpha \to 0$ 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.

21 pages, no figure, 2 misprints corrected; published version

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