Resonances for a semi-classical Schrödinger operator near a non trapping energy level
Summary: The author gives an example of a short range potential \(V\) 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 \(P=-h^2 \Delta+V\) 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.
scientific article; zbMATH DE number 1439796
scientific article