1-D Schroedinger operators with local interactions on a discrete set with unbounded potential

摘要

We study spectral properties of the one-dimensional Schrodinger operators H_(x,α,q) = -d~2/dx~2 q(x) +∑_(x_n ∈X)α_n δ(x - x_n) with local interactions, d_* = 0, and an unbounded potential q being a piecewise constant function, by using the technique of boundary triplets and the corresponding Weyl functions. Under various sufficient conditions for the self-adjointness and discreteness of Jacobi matrices, we obtain the condition of self-adjointness and discreteness for the operator H_(x,α,q).