Once Again On the Klein Paradox

TL;DR

This paper revisits the Klein Paradox, analyzing a modified Dirac equation with a focus on radial solutions and confinement properties in relativistic quantum mechanics.

Contribution

It introduces a detailed analysis of a modified Dirac equation derived from the Salpeter equation, highlighting differences in the kernel and confinement solutions.

Findings

Radial equation can be separated using standard momentum space methods.

Kernel differs from spinless Salpeter equation, affecting solutions.

Confined solutions exist for infinitely increasing potentials.

Abstract

After the short survey of the Klein Paradox in 3-dimensional relativistic equations, we present a detailed consideration of Dirac modified equation, which follows by one particle infinite overweighting in Salpeter Equation. It is shown, that the separation of angular variables and reduction to radial equation is possible by using standard methods in momentum space. The kernel of the obtained radial equation differs from that of spinless Salpeter equation in bounded regular factor. That is why the equation has solutions of confined type for infinitely increasing potential.