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arXiv · hep-th/0304174

Scattering and pair production by a potential barrier

A. I. Nikishov
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Abstract

Scattering and electron-positron pair production by a one-dimensional potential is considered in the framework of the $S-$matrix formalism. The solutions of the Dirac equation are classified according to frequency sign. The Bogoliubov transformation relating the in- and out-states are given. We show that the norm of a solution of the wave equation is determined by the largest amplitude of its asymptotic form when $x_3\to \pm\infty$. For a number of potentials we give the explicit expressions for the complete in- and out-sets of orthonormalized wave functions. We note that in principle virtual vacuum processes in external field influence the phase of wave function of scattered particle..

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A. I. Nikishov. 2003-04-21. Scattering and pair production by a potential barrier. https://doi.org/10.1134/1.1788038

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