The stability of the density of states of Schrödinger operator under very small perturbations
Let \(\Lambda_ L\) be a cube in \({\mathbb{R}}^ d\), \(d\geq 2\), of side legth L centered at the origin, \(H_ L\) be the restriction of the Schrödinger operator \(H=-\Delta +V_ 0\) to \(\Lambda_ L\), \(V_ L\) be a bounded non negative function with support in \(\Lambda_ L\). The behaviour of the function \(\phi_ L(E)=N(H_ L,E)-N(H_ L+V_ L,E)\) as \(L\to +\infty\) is considered, where N(A,E) denotes the number of eigenvalues of A not exceeding E.
scientific article; zbMATH DE number 4122494
scientific article