  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.
