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Infinite systems of potential wells. (English) Zbl 0808.35086
This article is a short presentation of the results obtained in the last twelve years in the semiclassical study of the tunneling effect for the Schrödinger operator. The emphasis is on results where near a given energy the energy surface has an infinite number of connected components. The author presents recent results obtained by U. Carlsson [Asymptotic Anal. 3, No. 3, 189-214 (1990; Zbl 0727.35094)] concerning a general reduction for the study of the spectrum at the bottom and by F. Klopp [Ann. Inst. Henri Poincaré, Phys. Théor. 55, No. 1, 459-509 (1991; Zbl 0754.35100)] who studies the perturbations of a periodic potential.
Reviewer: B.Helffer (Paris)
MSC:
35P15 Estimates of eigenvalues in context of PDEs
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
35Q40 PDEs in connection with quantum mechanics
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