Semi-classical asymptotics for magnetic bottles

Article type: Research Article

Authors: Truc, Françoise

Affiliations: Université de Grenoble I, Institut Fourier, Laboratoire de Mathématiques, UMR 5582 (CNRS-UJF) B.P. 74, 38402 St Martin d'Hères, France

Abstract: In this paper we investigate the asymptotic behaviour of the counting function of the eigenvalues for a semi-classical Schrödinger operator with a magnetic field, for a fixed energy, when the small parameter h goes to zero. We require for the magnetic field assumptions of the type “magnetic bottles” and we use a method of subdivision of Rd in cubes, in order to apply Courant's minimax variational principle. This method was previously used by Courant in the case of the classical counting function for minus Laplacian.

DOI: 10.3233/ASY-1997-153-408

Journal: Asymptotic Analysis, vol. 15, no. 3-4, pp. 385-395, 1997