  A generalized scattering amplitude where momenta of incoming-particles and
outgoing-particles as well as positions of incoming-particles and
outgoing-particles are specified is formulated. Idealistic beams and idealistic
measuring instruments where momenta and positions satisfy minimum uncertainty
are studied with a use of minimum wave packets, coherent states. In the present
work, we show general features of the generalized scattering amplitudes based
on ${\phi}^4$ theory. We give a proof of completeness of many body states,
asymptotic behaviors in the large distance region, and factorization of the
amplitudes. Despite of the non-orthogonal properties of wave packets, we found
that the probability interpretation is verified. A differential probability
depends upon the wave packet size but a total probability that is integrated in
the final states is independent from the size of final state wave packet and
becomes universal. Few body amplitudes are studied as examples.
