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Europhysics Letters (EPL)

Lie algebraic approach to singular oscillator with a position-dependent mass

Barnana Roy

Published Aug 30, 2005• 45 citations
Publisher

Abstract

We construct a singular-oscillator Hamiltonian with a position-dependent effective mass. It is shown that this quantum system admits a su (1,1) symmetry, and using this symmetry complete solution of the problem is obtained.
DOI
10.1209/epl/i2005-10212-2

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During recent years, exact solutions of position-dependent mass Schrödinger 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 ≥ 2 (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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