Klein–Gordon equations with homogeneous time-dependent electric fields

Abstract

We consider a system associated to Klein-Gordon equations with homogeneous time-dependent electric fields. The upper and lower boundaries of a time-evolution propagator for this system were proven by Veselić in 1991 for electric fields that are independent of time. We extend this result to time-dependent electric fields.

Scattering of a Klein–Gordon particle by a smooth barrier

“…The Klein-Gordon equation is used to describe spin-0 particles. This equation have been widely study in the literature for different physical systems both time-independent [1,2,3,4,5,6,7,8,9,10,11,12,13] and timedependent [14,15,16,17] Klein-Gordon equation. The analytical solution of the time-independent Klein-Gordon equation for different potentials has been caused of a lot of interest in recent years, for both bound states [2,3,6,9,12] and scattering solutions [1,4,5,7,8,9,10,11,13].…”