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Sur les singularités de Van Hove génériques. (On generic Van Hove singularities). (French) Zbl 0773.47034

This talk is devoted to the presentation of some properties of the Schrödinger operator with periodic electric potential on a lattice of \(\mathbb{R}^ d\) (with \(d=1,2\) or 3). In particular the author investigates the properties of the density of states and its singularities. These singularities are connected to the properties of the Floquet eigenvalues appearing in the Bloch theory and the author gives some generic properties of these eigenvalues (simplicity, Morse property …).
Reviewer: B.Helffer (Paris)

MSC:

47F05 General theory of partial differential operators
35J10 Schrödinger operator, Schrödinger equation
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References:

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