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Encadrement du N(\(\lambda\) ) pour un opérateur de Schrödinger avec un champ magnétique et un potentiel électrique. (Inclusion of N(\(\lambda\) ) for a Schrödinger operator with magnetic field and electric potential). (French) Zbl 0725.35068
The authors study the asymptotic behaviour at infinity of the number N(\(\lambda\)) of the eigenvalues in ]-\(\infty,\lambda]\) of the Schrödinger operator with magnetic field \(H=\sum^{n}_{j=1}(- i\partial_{x_ j}-a_ j(x))^ 2+V(x)\). Under regularity and increasing assumptions on V and the \(a_ j's\), they obtain upper and lower bounds for N(\(\lambda\)). These bounds are integrals of some quantities associated to V and the \(a_ j's\). Several examples are given where V and the \(a_ j's\) are polynomials.

MSC:
35P20 Asymptotic distributions of eigenvalues in context of PDEs
35J10 Schrödinger operator, Schrödinger equation
Keywords:
magnetic field
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