Parametric equations of motion for the transition operator and the Green's operator

A more comprehensive parametric equation of motion (PEM) approach to a general quantum many-body system for both discrete bound states and continuous scattering states is presented. For demonstration purposes, the derivation of PEMs for physically important quantities, the transition operator, and the Green's operator is outlined. It is shown that the PEMs can successfully replace the numerically difficult boundary value problem with an equivalent initial value problem.