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Advances in High Energy Physics
Volume 2018, Article ID 6405784, 8 pages
https://doi.org/10.1155/2018/6405784
Research Article

Spinors and Rodrigues Representations Associated with Orthogonal Polynomials

Department of Physics, Faculty of Basic Sciences, Shahed University, Tehran, Iran

Correspondence should be addressed to Zahra Bakhshi; ri.ca.dehahs@ihshkab.z

Received 26 December 2017; Revised 18 March 2018; Accepted 26 March 2018; Published 20 May 2018

Academic Editor: Shi-Hai Dong

Copyright © 2018 Zahra Bakhshi. 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

An effective approach is presented to produce Schrödinger-like equation for the spinor components from Dirac equation. Considering electrostatic potential as a constant value yields a second-order differential equation that is comparable with the well-known solvable models in the nonrelativistic quantum mechanics for the certain bound state energy spectrum and the well-known potentials. By this comparison, the gauge field potential and the relativistic energy can be written by the nonrelativistic models and the spinors will be related to the orthogonal polynomials. It has also shown that the upper spinors wave functions based on the orthogonal polynomials can be given in terms of the Rodrigues representations. Association with the Rodrigues representations of orthogonal polynomials has also been investigated in the lower spinor components, since they are related to the upper spinor components according to first-order differential equation that is attained from Dirac equation.