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

中国物理B ›› 2013, Vol. 22 ›› Issue (6): 60304-060304.doi: 10.1088/1674-1056/22/6/060304

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

H. Panahi, Z. Alizadeh

Department of Physics, University of Guilan, Rasht 51335-1914, Iran

收稿日期:2012-10-15 修回日期:2012-12-12 出版日期:2013-05-01 发布日期:2013-05-01

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

H. Panahi, Z. Alizadeh

Department of Physics, University of Guilan, Rasht 51335-1914, Iran

Received:2012-10-15 Revised:2012-12-12 Online:2013-05-01 Published:2013-05-01
Contact: H. Panahi, Z. Alizadeh E-mail:t-panahi@guilan.ac.ir; alizadeh52@yahoo.com

摘要/Abstract

摘要： 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.

关键词: superintegrable systems, constants of motion, deformed oscillator algebra, structure function

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.

Key words: superintegrable systems, constants of motion, deformed oscillator algebra, structure function

中图分类号: (Algebraic methods)

03.65.Fd

02.30.Ik (Integrable systems)

H. Panahi, Z. Alizadeh. Deformed oscillator algebra for quantum superintegrable systems in two-dimensional Euclidean space and on the complex two-sphere[J]. 中国物理B, 2013, 22(6): 60304-060304.

H. Panahi, Z. Alizadeh. Deformed oscillator algebra for quantum superintegrable systems in two-dimensional Euclidean space and on the complex two-sphere[J]. Chin. Phys. B, 2013, 22(6): 60304-060304.

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

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

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