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We consider a magnetic Schrodinger operator Hh on a compact Riemannian manifold, depending on the semiclassical parameter h > 0. We assume that there is no electric field. We suppose that the minimal value b0 of the intensity of the magnetic field b is strictly positive. We give a survey of the results on asymptotic behavior of the eigenvalues of the operator Hh in the semiclassical limit.

Semiclassical Spectral Asymptotics for a Magnetic Schrödinger Operator with Non-vanishing Magnetic Field