Danilov, L. I. 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. Cited in 7 Documents 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 Keywords:Schrödinger operator; spectrum; periodic electric potential; periodic magnetic potential; variable metric PDF BibTeX XML Cite \textit{L. I. Danilov}, Theor. Math. Phys. 134, No. 3, 392--403 (2003; Zbl 1178.35275); translation from Teor. Mat. Fiz. 134, No. 3, 447--459 (2003) Full Text: DOI