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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)
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
Full Text: DOI
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