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. 487–523DOI 10.2977/PRIMS/1195144421