Deformed oscillator algebra for quantum superintegrable systems in two-dimensional Euclidean space and on the complex two-sphere

doi:10.1088/1674-1056/22/6/060304

Abstract In this work, we study the superintegrable quantum systems in two-dimensional Euclidean space and on the complex two-sphere with second-order constants of the motion. We show that these constants of motion satisfy the deformed oscillator algebra. Then, we easily calculate the energy eigenvalues in an algebraic way by solving of a system of two equations satisfied by its structure function. The results are in agreement to the ones obtained from the solution of the relevant Schrödinger equation.

Keywords: superintegrable systems constants of motion deformed oscillator algebra structure function

Received: 15 October 2012
Revised: 12 December 2012
Accepted manuscript online:

PACS:	03.65.Fd	(Algebraic methods)
	02.30.Ik	(Integrable systems)

Corresponding Authors: H. Panahi, Z. Alizadeh
E-mail: t-panahi@guilan.ac.ir; alizadeh52@yahoo.com

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H. Panahi, Z. Alizadeh Deformed oscillator algebra for quantum superintegrable systems in two-dimensional Euclidean space and on the complex two-sphere 2013 Chin. Phys. B 22 060304

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Deformed oscillator algebra for quantum superintegrable systems in two-dimensional Euclidean space and on the complex two-sphere

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