Deformed oscillator algebras for two dimensional quantum superintegrable systems

Details Deformed oscillator algebras for two dimensional quantum superintegrable systems Deformed oscillator algebras for two dimensional quantum superintegrable systems

1993-09-16

arxiv.org/abs/hep-th/9309088v1

Phys. Rev. A 50 (1994) 3700

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, THES-TP 10/93, hep-the/yymmnnn

Scientific paper

10.1103/PhysRevA.50.3700

Quantum superintegrable systems in two dimensions are obtained from their classical counterparts, the quantum integrals of motion being obtained from the corresponding classical integrals by a symmetrization procedure. For each quantum superintegrable systema deformed oscillator algebra, characterized by a structure function specific for each system, is constructed, the generators of the algebra being functions of the quantum integrals of motion. The energy eigenvalues corresponding to a state with finite dimensional degeneracy can then be obtained in an economical way from solving a system of two equations satisfied by the structure function, the results being in agreement to the ones obtained from the solution of the relevant Schrodinger equation. The method shows how quantum algebraic techniques can simplify the study of quantum superintegrable systems, especially in two dimensions.

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