Sur le spectre semi-classique d'un syst\`eme int\'egrable de dimension 1 autour d'une singularit\'e hyperbolique

zbMATH Open1223.35126arXiv0811.2990MaRDI QIDQ3400262

Olivier Lablée

Publication date: 5 February 2010

Abstract: In this article we describe the semi-classical spectrum of a Schrodinger operator on $mathbbR$ with a double well potential. We study the shape of spectrum around the local maximum of the potential. In the classification of singularities of integrable systems, the double wells is the model of non-degenerate hyperbolic singularity.

Full work available at URL: https://arxiv.org/abs/0811.2990

zbMATH Keywords

Schrödinger operatorspectrum

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Schrödinger operator, Schrödinger equation (35J10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items (2)

On the semi-classical spectrum of an integrable system of dymension 1 around a hyperbolic singularity ⋮ The Maslov complex germ and semiclassical spectral series corresponding to singular invariant curves of partially integrable Hamiltonian systems

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