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

Abstract

Exact solutions of the Klein-Gordon equation for a charged particle in the presence of three spatially varying electromagnetic fields, namely,2x 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 ′ , b ′ ; 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.

Analytical solution of the Klein Gordon equation with a multi-parameter q-deformed Woods-Saxon type potential

“…Two of the authors of this paper, Ikot and Lütfüoglu, examined the KG equation solutions with an exponential-type molecule potential and discussed the thermodynamic properties in D dimensions [17]. Das and Arda obtained the exact solutions of the KG equation for a charged particle under a spatially varying electromagnetic field [18].…”

Pengaruh Medan Elektromagnet terhadap Partikel Dirac dan Klein-Gordon dalam Potensial Penghalang Periodik Satu Dimensi

“…Penyelesaian persamaan Klein-Gordon untuk partikel bermuatan dengan variasi medan elektromagnetik bisa dilakukan dengan menggunakan transformasi Laplace [12]. Penelitian lainnya dalam menyelesaian persamaan Dirac dan Klein-Gordon dengan potensial penghalang yang bergerak dengan kecepatan konstan , digunakan transformasi Lorentz untuk mengubah bentuk potensialnya ke dalam bentuk yang tidak bergantung waktu sehingga didapatkan koefisien refleksi dan transmisi [13].…”