This article is cited in 18 papers

The Spectrum of the Two-Dimensional Periodic Schrödinger Operator

L. I. Danilov

Physical-Technical Institute of the Ural Branch of the Russian Academy of Sciences

Abstract: The absence of eigenvalues (of infinite multiplicity) for the two-dimensional periodic Schrödinger operator with a variable metric is proved. The method of proof does not use the change of variables reducing the metric to a scalar form.

Keywords: Schrödinger operator, spectrum, periodic electric potential, periodic magnetic potential, variable metric.

Received: 10.01.2002
Revised: 13.06.2002

DOI: 10.4213/tmf160

 English version: Theoretical and Mathematical Physics, 2003, 134:3, 392–403

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