Finite rank approximation of wave operators for short-range and Coulomb interactions

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Abstract
For the two-body system wave operators are shown to be strongly approximatable by finite rank operators which are obtained from finite rank approximations of the full and asymptotic Hamiltonian in the sense of strong resolvent convergence. This is demonstrated for short-range potentials plus the Coulomb potential with expansion functions chosen in momentum space as step functions. A generalization to the N-body system is indicated.

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