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.
Corresponding Authors:
Sami Ortakaya
E-mail: samiortakaya@gmail.com
Cite this article:
Sami Ortakaya Exact solutions of the Klein–Gordon equation with ring-shaped oscillator potential by using the Laplace integral transform 2012 Chin. Phys. B 21 070303
[1]
Alhaidari A, Bahlouli B and Al-Hasan A 2006 Phys. Lett. A 349 87
[2]
Diao Y F, Yi L Z and Jia C S 2004 Phys. Lett. A 332 157
[3]
Chen G, Chen Z and Lou Z M 2004 Chin. Phys. 13 279
[4]
Qiang W C 2003 Chin. Phys. 12 136
[5]
Levai G 1992 J. Phys. A: Math. Gen. 25 L521
[6]
Yasuk F, Berkdemir C, Berkdemir A and Önem C 2005 Phys. Scr. 71 340
[7]
Yasuk F and Durmus A 2008 Phys. Scr. 77 015005
[8]
Quesne C A 1988 J. Phys. A: Math. Gen. 21 3093
[9]
Durmus A and Yasuk F 2007 J. Chem. Phys. 126 074108
[10]
Chen G 2004 Phys. Lett. A 326 55
[11]
Chen G 2004 Phys. Lett. A 328 123
[12]
Chen G 2005 Phys. Scr. 71 233
[13]
Ran Y, Xue L, Hu S and Su R K 2000 J. Phys. A: Math. Gen. 33 9265
[14]
Schiff J L 1999 The Laplace Transform: Theory and Applications (New York: Springer) p. 233
[15]
Chen C Y, Liu C L and Lu F L 2010 Phys. Lett. A 374 1346
[16]
Gradshteyn I S and Ryzhik I M 2007 Table of Integrals, Series, and Products (New York: Academic Press) p. 1171
[17]
Abramowitz M and Stegun I 1972 Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (Wa: Dover Publications) p. 1058
[18]
Lebedev N N 1965 Special Functions and Their Applications (New York: Prentice-Hall) p. 308
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