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The spectrum of the two-dimensional periodic Schrödinger operator. (English) Zbl 1178.35275
Theor. Math. Phys. 134, No. 3, 392-403 (2003); translation from Teor. Mat. Fiz. 134, No. 3, 447-459 (2003).
Summary: 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.

MSC:
35P05 General topics in linear spectral theory for PDEs
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
35J10 Schrödinger operator, Schrödinger equation
35Q40 PDEs in connection with quantum mechanics
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