Abstract

We consider the Schrödinger operator HηW=-δ+ηW, self-adjoint in L2(Rd), d≥1. Here η is a non-constant oscillating function, while W decays slowly and regularly at infinity. We study the asymptotic behaviour of the discrete spectrum of HηW near the origin, and due to the irregular decay of ηW, we encounter some non-semiclassical phenomena. In particular, HηW has less eigenvalues than suggested by the semiclassical intuition. © 2016 Elsevier Inc.