ON THE S-MATRIX OF SCHRODINGER OPERATOR WITH NONLOCAL δ-INTERACTION

Schrodinger operators with nonlocal delta-interaction are studied with the use of the Lax-Phillips scattering theory methods. The condition of applicability of the Lax-Phillips approach in terms of non-cyclic functions is established. Two formulas for the S-matrix are obtained. The first one deals with the Krein-Naimark resolvent formula and the Weyl-Titchmarsh function, whereas the second one is based on modified reflection and transmission coefficients. The S-matrix S(z) is analytical in the lower half-plane C_ when the Schrodinger operator with nonlocal delta-interaction is positive self-adjoint. Otherwise, S(z) is a meromorphic matrix-valued function in C_ and its properties are closely related to the properties of the corresponding Schrodinger operator. Examples of S-matrices are given.