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Séminaire de EDP - Physique Mathématique

On the spectrum of the Schroedinger operator on $Pi^d$: a normal form approach

D. Bambusi

Salle de Conférences

le 24 septembre 2019 à 11:30

I will present a new method based on normal form and pseudodifferential calculus to get spectral results on Schroedinger type operators on Πd\Pi^d. In the one dimensional case one obtains in a very simple way the classical result that the eigenvalues of a Schroedinger operator come in couple which are well separated one from the others and such that the two eigenvalues in a couple have the same asymptotic. In the higher dimensional case I will show how to obtain the asymptotic behavior of a large part of the spectrum of Schroedinger operators and prove some properties similar to those just described for the one dimensional case. Joint work with Beatrice Langella and Riccardo Montalto