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Semiclassical analysis for the ground state energy of a Schrödinger operator with magnetic wells. (English) Zbl 0851.58046

Motivated by a recent paper by R. Montgomery [Commun. Math. Phys. 168, No. 3, 651-675 (1995; Zbl 0827.58076)], we give the asymptotic behavior, in the semi-classical sense, of the ground state energy for the Schrödinger operator with a magnetic field. We consider the case when the locus of the minima of the intensity of the magnetic field is compact and our study is sharper when this locus is a hypersurface or a finite union of points.
Reviewer: M.Biroli (Monza)

MSC:

58J50 Spectral problems; spectral geometry; scattering theory on manifolds
35P05 General topics in linear spectral theory for PDEs
58Z05 Applications of global analysis to the sciences
82D40 Statistical mechanics of magnetic materials

Citations:

Zbl 0827.58076
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