NOTE ON THE SPECTRAL CONCENTRATION FOR THE SCHRÖDINGER OPERATOR WITH POINT INTERACTION

Abstract

In this paper the family of the Schrödinger operator $H_k=-d^2/d{x}^2+q(x)+\delta (x-1)/k$ in $L^2(0,\infty )$ is investigated. Roughly speaking, if $q(x)=o(x^{-2})$, then the spectral concentration occurs as $k\to 0$.