Group C*-Algebras and the Spectrum of a Periodic Schrödinger Operator on a Manifold

Sunada, Toshikazu

Canadian journal of mathematics, Tome 44 (1991) no. 1, pp. 180-193

Résumé

The spectrum of the Laplacian or more generally of a Schrödinger operator on an open manifold may have possibly a complicated aspect. For example, a Cantor set in the real axis may appear as the spectrum even for an innocent looking potential on a standard Riemannian manifold (see J. Moser [10]). The fundamental result of the spectral theory of periodic Schrödinger operators, however, says that the picture of the spectrum of a Schrödinger operator on Rn with a periodic potential is simple; indeed the spectrum consists of a series of closed intervals of the real axis without accumulation, separated in general by gaps outside the spectrum (see M. Reed and B. Simon [13] or M. M. Skriganov [15] for instance).

Détail

DOI : 10.4153/CJM-1992-011-3

Mots-clés : 58G25, 47C15

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