## An infinite number of wells in the semi-classical limit.(English)Zbl 0727.35094

This paper analyzes the spectrum of the Schrödinger operator $$-h^ 2\Delta +V$$ on $${\mathbb{R}}^ n$$. The author extends previous results (finite number of wells) by B. Helffer and J. Sjöstrand [Commun. Partial Differ. Equations 9, 337-408 (1984; Zbl 0546.35053)] to the case of a potential V with an infinite number of well separated wells. This contains in particular a result obtained by A. Outassourt [J. Funct. Anal. 72, 65-93 (1987; Zbl 0662.35023)] corresponding to a compact perturbation of a periodic potential.
Reviewer: B.Helffer (Paris)

### MSC:

 35P05 General topics in linear spectral theory for PDEs 81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory 35J10 Schrödinger operator, Schrödinger equation

### Keywords:

infinite number of wells

### Citations:

Zbl 0546.35053; Zbl 0662.35023