  This article describes a method for calculating S-matrix elements using
Hamiltonians obtained in the renormalization group procedure for effective
particles. It is shown that the scattering amplitudes obtained using a
canonical Hamiltonian $H^\Delta$ with counterterms are the same as those
obtained using a renormalized Hamiltonian for effective particles, $H_\lambda$.
The result is independent of the ultraviolet cutoff $\Delta$ and the
renormalization-group parameter $\lambda$.
