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

Abstract

Exact solutions of the Klein-Gordon equation for a charged particle in the presence of three spatially varying electromagnetic fields, namely, (i) $\vec{E}=\alpha {\beta }_0{e}^{-\alpha x_2}{\hat{x}}_2$, $\vec{B}=\alpha {\beta }_1{e}^{-\alpha x_2}{\hat{x}}_3$ (ii) $\vec{E}=\frac{{\beta }_0^{{}^{\prime }}}{x_2^2}{\hat{x}}_2$, $\vec{B}=\frac{{\beta }_1^{{}^{\prime }}}{x_2^2}{\hat{x}}_3$, and (iii) $\vec{E}=\frac{2{\beta }_0^{{}^{\prime }}}{x_2^3}{\hat{x}}_2$, $\vec{B}=\frac{2{\beta }_1^{{}^{\prime }}}{x_2^3}{\hat{x}}_3$, are studied. All these fields are generated from a systematic study of a particular type of differential equation whose coefficients are linear in independent variable. The Laplace transform approach is used to find the solutions and the corresponding eigenfunctions are expressed in terms of the hypergeometric functions ${}_1{F}_1(a^{\prime },b^{\prime };x)$ for 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

16 pages

References in corpus (3)

• Exact Solutions of the Schrödinger Equation via Laplace Transform Approach: Pseudoharmonic potential and Mie-type potentials
• Shape invariance approach to exact solutions of the Klein-Gordon equation
• A Laplace transform approach to find the exact solution of the N-dimensional Schrödinger equation with Mie-type potentials and construction of Ladder operators

Cited by in corpus (1)

• Analytical solution of the Klein Gordon equation with a Multi-parameter q-Deformed Woods-Saxon Type Potential