  A general approach to a solution of few- and many-body scattering problems
based on a continuum-discretization procedure is described in detail. The
complete discretization of continuous spectrum is realized using stationary
wave packets which are the normalized states constructed from exact
non-normalized continuum states. Projecting the wave functions and all
scattering operators like $t$-matrix, resolvent, etc. on such a wave-packet
basis results in a formulation of quantum scattering problem entirely in terms
of discrete elements and linear equations with regular matrices. It is
demonstrated that there is a close relation between the above stationary wave
packets and pseudostates which are employed often to approximate the scattering
states with a finite $L_2$ basis. Such a fully discrete treatment of
complicated few- and many-body scattering problems leads to significant
simplification of their practical solution. Also we get finite-dimensional
approximations for complicated operators like effective interactions between
composite particles constructed via the Feshbach-type projection formalism. As
illustrations to this general approach we consider several important particular
problems including multichannel scattering and scattering in the three-nucleon
system within the Faddeev framework.
