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On absolute continuity of spectra of periodic elliptic operators. (English) Zbl 0965.35100

Dittrich, Jaroslav (ed.) et al., Mathematical results in quantum mechanics. QMath7 conference, Prag, Czech Republic, June 22-26, 1998. Basel: Birkhäuser. Oper. Theory, Adv. Appl. 108, 291-297 (1999).
The paper contains a brief description of a simplified version of A. Sobolev’s proof of absolute continuity for the spectra of periodic magnetic Schrödinger operators. This approach is in principle applicable to all periodic elliptic operators known to be of interest for mathematical physics (including Maxwell), and in all these cases leads to the same model problem in complex analysis.
For the entire collection see [Zbl 0911.00055].

MSC:

35P05 General topics in linear spectral theory for PDEs
35J10 Schrödinger operator, Schrödinger equation
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