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Pólya’s conjecture in the presence of a constant magnetic field. (English) Zbl 1179.35205

Summary: We consider the Dirichlet Laplacian with a constant magnetic field in a two-dimensional domain of finite measure. We determine the sharp constants in semi-classical eigenvalue estimates and show, in particular, that Pólya’s conjecture is not true in the presence of a magnetic field.

MSC:

35P15 Estimates of eigenvalues in context of PDEs
35J10 Schrödinger operator, Schrödinger equation
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