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MP: Theoretische und Mathematische Grundlagen der Physik

MP 6: Wave Equations and Scattering Theory

MP 6.1: Fachvortrag

Mittwoch, 9. März 2005, 12:05–12:25, TU MA043

“Normalization” and “Completeness” of the Volkov Solutions — •Stephan Zakowicz — Institut für Theoretische Physik, Justus-Liebig-Universität Giessen, Heinrich-Buff-Ring 16, 35392 Gießen

The (non-square-integrable) Volkov solutions [1] fulfil the Dirac equation for a charged spin-1/2 particle in the field of a classical plane electromagnetic wave.

It was demonstrated before [2] that under certain assumptions on the external electromagnetic vector potential, square-integrable wave packets may be constructed from these Volkov solutions. Two commonly believed conjectures have been rigorously proved by the author recently and will be discussed in this contribution [3]: (1) Wave packets from “electronic” and “positronic” Volkov solutions are orthogonal to each other when the vector potential and its first derivative are bounded; this fact leads to the correct “normalization” of wave packets. (2) On the same assumptions as in (1), the wave packets fulfil the Dirac equation.

Apart from the “normalization” of the Volkov solutions, their “completeness” is also of relevance for the computation of physical processes. The current state of a possible proof of this supposition is briefly addressed.

[1] D. M. Wolkow, Z. Phys. 94, 250 (1935)

[2] S. Zakowicz, Verhandl. DPG (VI) 39, 5/2004, p. 27

[3] S. Zakowicz, J. Math. Phys. (in print, 2005); Preprint: http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=04-234