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Open Quantum Systems Decoherence

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

arXiv
Authors: Tapas Das, Altug Arda

Year

2016

Paper ID

42010

Status

Preprint

Abstract Read

~2 min

Abstract Words

146

Citations

N/A

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}=αβ0e-αx2hat{x}2, vec{B}=αβ1e-αx2hat{x}3 (ii) vec{E}=frac{β0'}{x22}hat{x}2, vec{B}=frac{β1'}{x22}hat{x}3, and (iii) vec{E}=frac{2β0'}{x23}hat{x}2, vec{B}=frac{2β1'}{x23}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 1F1(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, Jn(x), for the last case

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  • Exact solutions of the Klein-Gordon equation for a charged particle in the presence of three spatially varying electromagnetic fields, namely, (i) vecE=αβ0e^-αx2hatx2...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1612.02293 [2] arXiv https://arxiv.org/abs/1612.02293 [3] Publisher https://arxiv.org/abs/1612.02293

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