Klein-Gordon equation for a charged particle in space-varying electromagnetic fields-A systematic study via the Laplace transform

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DAS T., Arda A.

CHINESE JOURNAL OF PHYSICS, vol.55, no.2, pp.310-317, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 55 Issue: 2
  • Publication Date: 2017
  • Doi Number: 10.1016/j.cjph.2016.12.008
  • Journal Name: CHINESE JOURNAL OF PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.310-317
  • Keywords: Laplace transformation approach, Klein-Gordon equation, Electromagnetic field, SCHRODINGER-EQUATION, MOTION, WAVE, POTENTIALS, SCALAR
  • Hacettepe University Affiliated: Yes

Abstract

Exact solutions of the Klein-Gordon equation for a charged particle in the presence of three spatially varying electromagnetic fields, namely, (i) (E) over right arrow = alpha beta(0)e(-alpha x2)(x) over cap (2), (B) over right arrow = alpha beta(1)e(-alpha x2)(x) over cap (3) (ii) (E) over right arrow = beta '(0)/x(2)(2)(x) over cap (2), (B) over right arrow = beta '(1)/x(2)(2) (x) over cap (3), (iii) (E) over right arrow = 2 beta '(0)/x(2)(3)(x) over cap (2), (B) over right arrow = 2 beta '(1)/x(2)(3)(x) over cap (3), are studied. All these fields are generated from a systematic study of a particular type of differential equation whose coefficients are linear in the independent variable. The Laplace transform approach is used to find the solutions, and the corresponding eigenfunctions are expressed in terms of the hypergeometric functions F-1(1) (a ', b '; x) for the first two cases of the above configurations, while the same are expressed in terms of the Bessel functions of first kind, J(n)(x), for the last case. (C) 2017 The Physical Society of the Republic of China (Taiwan). Published by Elsevier B. V. All rights reserved.