Quadratic algebras and position-dependent mass Schrödinger equations

Physics – Mathematical Physics

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6 pages, no figure, communication at the 5th Int. Symp. on Quantum Theory and Symmetries (QTS5), Valladolid, Spain, July 22-28

Scientific paper

During recent years, exact solutions of position-dependent mass Schr\"odinger equations have inspired intense research activities, based on the use of point canonical transformations, Lie algebraic methods or supersymmetric quantum mechanical techniques. Here we highlight the interest of another approach to such problems, relying on quadratic algebras. We illustrate this point by constructing spectrum generating algebras for a class of $d$-dimensional radial harmonic oscillators with $d\ge2$ (including the one-dimensional oscillator on the line via some minor changes) and a specific mass choice. This provides us with a counterpart of the well-known su(1,1) Lie algebraic approach to the constant-mass oscillators.

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