Multi-dimensional Schrödinger operators with point interactions - Goloshchapova, N. (Methods of Functional Analysis and Topology, 2011)
We study two- and three-dimensional matrix Schrödinger operators with mN point interactions. Using the technique of boundary triplets and the corresponding Weyl functions, we complete and generalize the results obtained by the other authors in this field. For instance, we parametrize all self-adjoint extensions of the initial minimal symmetric Schrödinger operator by abstract boundary conditions and characterize their spectra. Particularly, we find a sufficient condition in terms of distances and intensities for the self-adjoint extension H_α,X^(3) to have m’ negative eigenvalues, i.e., κ_-(H_α,X^(3))=m’m. We also give an explicit description of self-adjoint nonnegative extensions.