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Open Quantum Systems Decoherence

Spectrum generating algebras for position-dependent mass oscillator Schrodinger equations

arXiv
Authors: C. Quesne

Year

2007

Paper ID

50395

Status

Preprint

Abstract Read

~2 min

Abstract Words

116

Citations

N/A

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 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 ge 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.

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  • The interest of quadratic algebras for position-dependent mass Schrödinger equations is highlighted by constructing spectrum generating algebras for a class of d-dimensional...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:0705.0862 [2] arXiv https://arxiv.org/abs/0705.0862 [3] Publisher https://arxiv.org/abs/0705.0862

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