On the number of negative eigenvalues of a multi-dimensional Schrodinger operator with point interactions - Ogurisu, O. (Methods of Functional Analysis and Topology, 2010)
We prove that the number N of negative eigenvalues of a Schrödinger operator L with finitely many points of δ-interactions on R^d (d3) is equal to the number of negative eigenvalues of a certain class of matrix M up to a constant. This M is expressed in terms of distances between the interaction points and the intensities. As applications, we obtain sufficient and necessary conditions for L to satisfy N=m,n,n for d=1,2,3, respectively, and some estimates of the minimum and maximum of N for fixed intensities. Here, we denote by n and m the numbers of interaction points and negative intensities, respectively.