# Resonances for a Semi-Classical Schrödinger Operator Near a Non Trapping Energy Level

### Michel Rouleux

CNRS Luminy, Marseille, France

## Abstract

We give an example of a short range potential F on the real line that is dilation analytic at infinity, non trapping at energy *E*>0, but oscillating in the neighborhood of some points, so rapidly that the Schrödinger operator *P*=-_h_2Δ+*V* shows a string of resonances near *E* in the lower half plane when *h*>0 is small enough. The extended states behave as standing waves partially reflected off the bumps of *V*. Such a potential is the analogue of the Wigner-Von Neumann potential in the case of embedded eigenvalues.

## Cite this article

Michel Rouleux, Resonances for a Semi-Classical Schrödinger Operator Near a Non Trapping Energy Level. Publ. Res. Inst. Math. Sci. 34 (1998), no. 6, pp. 487–523

DOI 10.2977/PRIMS/1195144421