Infinite systems of potential wells (Q1333781)

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 \textit{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 \textit{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.