The Dirac Equation and its Solutions by Bagrov Vladislav G.;Gitman Dmitry

Author:Bagrov, Vladislav G.;Gitman, Dmitry
Language: eng
Format: epub
Publisher: De Gruyter
Published: 2014-07-05T00:00:00+00:00

Equation (5.25) gives, in this case, a solution to equation (5.22) providing one sets

(5.36)

As for the function ϕ(u0), it remains arbitrary. A physically important peculiarity of this solution is that when the potential A(u0 ) (5.33) is periodic, the function a(u0 ) and the vector b(u0 ) (as well as the spinor V thereof) are generally no longer periodic functions of u0 (they are, instead, the so-called almost-periodic functions). Therefore, the presence of anomalous moments results, in this case, in solutions that do not possess the periodicity properties even though the wave is periodic. No other types of external fields of the form (5.33) have yet been found for which exact solutions of the Dirac–Pauli equation for a charged particle are known.

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