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Spectrum generating algebras for position-dependent mass oscillator Schrödinger equations

par Quesne, Christiane
Référence Journal of Physics A: Mathematical and Theoretical, 40, 43, page (13107-13119)
Publication Publié, 2007-10

Article révisé par les pairs

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Résumé :

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 ≥ 2 and a specific mass choice depending on some positive parameter α. 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 α → 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. © 2007 IOP Publishing Ltd.