  The projection formalism for calculating effective Hamiltonians and
resonances is generalized to the nonlocal and/or nonhermitian case, so that it
is applicable to the reduction of relativistic systems (Bethe-Salpeter
equations), and to dissipative systems modeled by an optical potential.
  It is also shown how to recover all solutions of the time-independent
Schroedinger equation in terms of solutions of the effective Schroedinger
equation in the reduced state space and a Schroedinger equation in a reference
state space.
  For practical calculations, it is important that the resulting formulas can
be used without computing any projection operators. This leads to a modified
coupled reaction channel/resonating group method framework for the calculation
of multichannel scattering information.
