In- and out-states of scalar particles confined between two capacitor plates

Abstract

In the present article, using a non-commutative integration method of linear differential equations, we, considering the Klein-Gordon equation with the $L$-constant electric field with large $L$ and using the light cone variables, find new complete sets of its exact solutions. These solutions can be related by integral transformations to previously known solutions that were found in Phys. Rev. D. $\text{93}$, 045033(2016). Then, using the general theory developed in Phys. Rev. D. $\text{93}$, 045002 (2016), we construct (in terms of the new solutions) the so-called in- and out-states of scalar particles confined between two capacitor plates.

9 pages, misprints corrected. arXiv admin note: substantial text overlap with arXiv:1903.06832, misprint corrected

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