Pseudo-Harmonic Oscillatory Ring-Shaped Potential in a Relativistic Equation
M. Eshghi**
1 Department of Physics, Faculty of Sciences, Imam Hossein Comprehensive University, Tehran, Iran
Abstract ：Exact solutions of the Dirac equation are studied for the pseudo-harmonic oscillatory ring-shaped potential by using the Laplace transform approach and the Nikiforov–Uvarov (NU) method. The normalized eigenfunctions are expressed in terms of hyper-geometric series and use the NU and Laplace methods to obtain the eigenvalues equations. The obtained result of the eigenvalue equation is compared. At the end, one can find with a simple transformation the lower spinor component of the Dirac equation.
收稿日期: 2012-06-29
出版日期: 2012-11-28
:
03.65.Pm
(Relativistic wave equations)
03.65.Ge
(Solutions of wave equations: bound states)
02.30.Gp
(Special functions)
[1] Salamin, Y I, Hu S, Hatsagortsyan K Z and Keitel C H 2006 Phys. Rep. 427 41 2009 Chin. Phys. Lett. 26 011201 2009 Chin. Phys. Lett. 26 054101 2006 Nat. Phys. 2 620 1988 Phys. Rev. D 38 348 2010 Ann. Phys. 325 2522 2012 Commun. Theor. Phys. 57 355 2012 Few-Body Syst. 52 41 Int. J. Sci. Adv. Tech. 1(10) 112012 J. Math. Phys. 53 082101 Chin. J. Phys. 50 5332005 Chin. Phys. 14 42 2012 Ann. Phys. 327 841 Chin. J. Phys. 45 4802010 Commun. Theor. Phys. 53 242 2009 Phys. Lett. A 373 616 2010 Ann. Phys. 325 373 Int. J. Phys. Sci. 6 38072010 Phys. Lett. A 374 704 2005 Chin. Phys. 14 1075 Guide to the Applications of Laplace Transforms (Princeton: Princeton University Press)2004 Phys. Lett. A 326 55 2012 J. Math. Chem. 50 971 Ann. Phys. 79 3611991 J. Phys. A: Math. Gen. 24 79 2005 Chin. Phys. 14 1075 2004 Phys. Rev. C 69 024319 2009 Phys. Lett. A 373 616 Schaum's Outline of Theory and Problems of Laplace Transforms (New York: Schaum Publishing)Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (New York: Dover)Special Functions of Mathematical Physics (Verlag Basel: Birkhauser)2009 Phys. Scr. 80 015001
[1]
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[2]
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[3]
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[4]
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[5]
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[6]
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2012, Vol. 29 
