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We study a class of self-adjoint operators defined on the direct sum of twoHilbert spaces: a finite dimensional one called sometimes a ``small subsystem''and an infinite dimensional one -- a ``reservoir''. The operator, which we calla ``Friedrichs Hamiltonian'', has a small coupling constant in front of itsoff-diagonal term. It is well known that under some conditions in the weakcoupling limit the appropriately rescaled evolution in the interaction pictureconverges to a contractive semigroup when restricted to the subsystem. We showthat in this model, the properly renormalized and rescaled evolution convergeson the whole space to a new unitary evolution, which is a dilation of the abovementioned semigroup. Similar results have been studied before \cite{AFL} inmore complicated models and they are usually referred to as "stochastic Limit".Comment: changes in notation and title, minor correction

Extended weak coupling limit for Friedrichs Hamiltonians