Effective Schroedinger equations for nonlocal and/or dissipative systems

摘要

The projection formalism for calculating effective Hamiltonians andresonances is generalized to the nonlocal and/or nonhermitian case, so that itis applicable to the reduction of relativistic systems (Bethe-Salpeterequations), and to dissipative systems modeled by an optical potential. It is also shown how to recover all solutions of the time-independentSchroedinger equation in terms of solutions of the effective Schroedingerequation in the reduced state space and a Schroedinger equation in a referencestate space. For practical calculations, it is important that the resulting formulas canbe used without computing any projection operators. This leads to a modifiedcoupled reaction channel/resonating group method framework for the calculationof multichannel scattering information.