SINGULAR SCHRODINGER-OPERATORS AS LIMITS OF POINT INTERACTION HAMILTONIANS

In this paper we give results on the approximation of (generalized) Sc hrodinger operators of the form -Delta + mu for some finite Radon meas ure mu on R-d. For d = 1 we shall show that weak convergence of measur es mu(n) to mu implies norm resolvent convergence of the operators -De lta + mu(n) to -Delta + mu. In particular Schrodinger operators of the form -Delta + mu for some finite Radon measure mu can be regularized or approximated by Hamiltonians describing point interactions. For d = 3 we shall show that a fairly large class of singular interactions ca n be regarded as limit of point interactions.