ar X iv : 0 81 2 . 50 38 v 1 [ m at h . SP ] 3 0 D ec 2 00 8 SEMICLASSICAL ANALYSIS OF SCHRÖDINGER OPERATORS WITH MAGNETIC WELLS
نویسندگان
چکیده
We give a survey of some results, mainly obtained by the authors and their collaborators, on spectral properties of the magnetic Schrödinger operators in the semiclassical limit. We focus our discussion on asymptotic behavior of the individual eigenvalues for operators on closed manifolds and existence of gaps in intervals close to the bottom of the spectrum of periodic operators.
منابع مشابه
m at h . SP ] 1 8 M ar 2 00 1 SEMICLASSICAL ASYMPTOTICS AND GAPS IN THE SPECTRA OF MAGNETIC SCHRÖDINGER OPERATORS
In this paper, we study an L version of the semiclassical approximation of magnetic Schrödinger operators with invariant Morse type potentials on covering spaces of compact manifolds. In particular, we are able to establish the existence of an arbitrary large number of gaps in the spectrum of these operators, in the semiclassical limit as the coupling constant μ goes to zero.
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