Effective Schroedinger equations for nonlocal and/or dissipative systems
  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. 
Arnold Neumaier