Helffer, Bernard; Mohamed, Arbderemane Semiclassical analysis for the ground state energy of a Schrödinger operator with magnetic wells. (English) Zbl 0851.58046 J. Funct. Anal. 138, No. 1, 40-81 (1996). 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) Cited in 1 ReviewCited in 54 Documents 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 Keywords:asymptotic behavior; ground state energy; Schrödinger operator; magnetic field Citations:Zbl 0827.58076 × Cite Format Result Cite Review PDF Full Text: DOI Link