Singular Schrödinger Operators as Limits Point Interaction Hamiltonians

In this paper we give results on the approximation of (generalized) Schrödinger operators of the form - ▵ + µ for some finite Radon measure µ on Rd. For d = 1 we shall show that weak convergence of measures µn to µ implies norm resolvent convergence of the operators -▵ + µn to -▵ + µ. In particular Schrödinger operators of the form - ▵ + µ for some finite Radon measure µ can be regularized or approximated by Hamiltonians describing point interactions. For d = 3 we shall show that a fairly large class of singular interactions can be regarded as limit of point interactions.