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Advances in High Energy Physics
Volume 2015 (2015), Article ID 612757, 8 pages
http://dx.doi.org/10.1155/2015/612757
Research Article

Exact Solution of the Curved Dirac Equation in Polar Coordinates: Master Function Approach

Department of Physics, University of Guilan, Rasht 41635-1914, Iran

Received 6 February 2015; Accepted 25 April 2015

Academic Editor: Ming Liu

Copyright © 2015 H. Panahi and L. Jahangiri. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Abstract

We show that the () curved Dirac equation in polar coordinates can be transformed into Schrodinger-like differential equation for upper spinor component. We compare this equation with the Schrodinger equation derived from shape invariance property of second order differential equations of mathematical physics. This formalism enables us to determine the electrostatic potential and relativistic energy in terms of master function and corresponding weight function. We also obtain the spinor wave function in terms of orthogonal polynomials.