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

TL;DR

This paper derives exact solutions for the Klein-Gordon equation in a confined electric field, constructing in- and out-states of scalar particles between capacitor plates using a novel non-commutative integration method.

Contribution

It introduces a new non-commutative integration method to find exact solutions and constructs in- and out-states for scalar particles in a confined electric field.

Findings

Derived new complete sets of exact solutions using the non-commutative method.

Related solutions to previous known solutions via integral transformations.

Constructed in- and out-states of scalar particles confined between 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. $\textbf{93}$, 045033(2016). Then, using the general theory developed in Phys. Rev. D. $\textbf{93}$, 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.