Exact solutions of the Klein–Gordon equation with ring-shaped oscillator potential by using the Laplace integral transform

doi:10.1088/1674-1056/21/7/070303

中国物理B ›› 2012, Vol. 21 ›› Issue (7): 70303-070303.doi: 10.1088/1674-1056/21/7/070303

Exact solutions of the Klein–Gordon equation with ring-shaped oscillator potential by using the Laplace integral transform

Sami Ortakaya

Institute of Natural and Applied Sciences, Erciyes University, 38039 Kayseri, Turkey

收稿日期:2011-11-29 修回日期:2012-01-03 出版日期:2012-06-01 发布日期:2012-06-01

Exact solutions of the Klein–Gordon equation with ring-shaped oscillator potential by using the Laplace integral transform

Sami Ortakaya^†

Institute of Natural and Applied Sciences, Erciyes University, 38039 Kayseri, Turkey

Received:2011-11-29 Revised:2012-01-03 Online:2012-06-01 Published:2012-06-01
Contact: Sami Ortakaya E-mail:samiortakaya@gmail.com

摘要/Abstract

摘要： We present exact solutions for the Klein--Gordon equation with a ring-shaped oscillator potential. The energy eigenvalues and the normalized wave functions are obtained for a particle in the presence of non-central oscillator potential. The angular functions are expressed in terms of the hypergeometric functions. The radial eigenfunctions have been obtained by using the Laplace integral transform. By means of the Laplace transform method, which is efficient and simple, the radial Klein--Gordon equation is reduced to a first-order differential equation.

关键词: ring-shaped oscillator, Klein--Gordon equation, Laplace integral transform, bound states

Abstract: We present exact solutions for the Klein--Gordon equation with a ring-shaped oscillator potential. The energy eigenvalues and the normalized wave functions are obtained for a particle in the presence of non-central oscillator potential. The angular functions are expressed in terms of the hypergeometric functions. The radial eigenfunctions have been obtained by using the Laplace integral transform. By means of the Laplace transform method, which is efficient and simple, the radial Klein--Gordon equation is reduced to a first-order differential equation.

Key words: ring-shaped oscillator, Klein--Gordon equation, Laplace integral transform, bound states

中图分类号: (Solutions of wave equations: bound states)

03.65.Ge

03.65.Pm (Relativistic wave equations)

Sami Ortakaya . Exact solutions of the Klein–Gordon equation with ring-shaped oscillator potential by using the Laplace integral transform[J]. 中国物理B, 2012, 21(7): 70303-070303.

Sami Ortakaya . Exact solutions of the Klein–Gordon equation with ring-shaped oscillator potential by using the Laplace integral transform[J]. Chin. Phys. B, 2012, 21(7): 70303-070303.

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Exact solutions of the Klein–Gordon equation with ring-shaped oscillator potential by using the Laplace integral transform

Exact solutions of the Klein–Gordon equation with ring-shaped oscillator potential by using the Laplace integral transform

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