zbMATH — the first resource for mathematics

Semiclassical analysis for the Schrödinger operator with magnetic wells (after R. Montgomery, B. Helffer-A. Mohamed). (English) Zbl 0887.35131
Rauch, Jeffrey (ed.) et al., Quasiclassical methods. Proceedings based on talks given at the IMA workshop, Minneapolis, MN, USA, May 22–26, 1995. New York, NY: Springer. IMA Vol. Math. Appl. 95, 99-114 (1997).
Summary: We present some survey on the semiclassical analysis of the Schrödinger operator with magnetic fields with emphasis on the recent results by R. Montgomery and extensions obtained in collaboration with A. Mohamed. The main point is the analysis of the asymptotic behavior, in the semiclassical 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.
For the entire collection see [Zbl 0878.00062].
Reviewer: Reviewer (Berlin)

35Q40 PDEs in connection with quantum mechanics
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory