Comptes Rendus
Spectral asymptotics for magnetic Schrödinger operators with rapidly decreasing electric potentials
[Asymptotiques spectrales pour des opérateurs magnétiques de Schrödinger avec des potentiels électriques qui décroissent rapidement à l'infini]
Comptes Rendus. Mathématique, Volume 335 (2002) no. 8, pp. 683-688.

On considère l'opérateur de Schrödinger H(V) agissant dans L 2 ( 2 ) ou L 2 ( 3 ) avec un champ magnétique constant et un potentiel électrique V qui génériquement décroı̂t à l'infini exponentiellement vite ou est à un support compact. On étudie le comportement asymptotique du spectre discret de H(V) en voisinage des points de la frontière de son spectre essentiel. Si la décroissance de V est gaussienne ou plus rapide ce comportement ne se décrit pas par les formules semi-classiques connues dans le cas où V décroı̂t comme une puissance.

We consider the Schrödinger operator H(V) on L 2 ( 2 ) or L 2 ( 3 ) with constant magnetic field, and a class of electric potentials V which typically decay at infinity exponentially fast or have a compact support. We investigate the asymptotic behaviour of the discrete spectrum of H(V) near the boundary points of its essential spectrum. If V decays like a Gaussian or faster, this behaviour is non-classical in the sense that it is not described by the quasi-classical formulas known for the case where V admits a power-like decay.

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DOI : 10.1016/S1631-073X(02)02554-2

Georgi D. Raikov 1 ; Simone Warzel 2

1 Departamento de Matemáticas, Universidad de Chile, Las Palmeras 3425, Casilla 653, Santiago, Chile
2 Institut für Theoretische Physik, Universität Erlangen-Nürnberg, Staudtstrasse 7, 91058 Erlangen, Germany
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     title = {Spectral asymptotics for magnetic {Schr\"odinger} operators with rapidly decreasing electric potentials},
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Georgi D. Raikov; Simone Warzel. Spectral asymptotics for magnetic Schrödinger operators with rapidly decreasing electric potentials. Comptes Rendus. Mathématique, Volume 335 (2002) no. 8, pp. 683-688. doi : 10.1016/S1631-073X(02)02554-2. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02554-2/

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