 97396 J.F. Brasche, R. Figari, A. Teta
 Singular Schr{\"o}dinger Operators as Limits of Point Interaction
Hamiltonians.
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Jul 7, 97

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Abstract. In this paper we give results on the approximation of (generalized)
Schr{\"o}dinger operators of the form $\Delta + \mu$ for some finite
Radon measure $\mu$ on ${\bf R}^d$. For $d=1$ we shall show that weak
convergence of measures $\mu_n$ to $\mu$ implies norm resolvent
convergence of the operators $\Delta + \mu_n$ to $\Delta + \mu$.
In particular
Schr{\"o}dinger 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 can be regarded as limit of point
interactions.
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