Exact scattering solutions in an energy sudden (ES) representation

In this paper, we lay down the theoretical foundations for computing exact scattering wave functions in a reference frame which moves in unison with the system internal coordinates. In this frame the (internal) coordinates appear to be fixed and its adoption leads very naturally (in zeroth order) to the energy sudden (ES) approximation [and the related infinite order sudden (IOS) method]. For this reason we call the new representation for describing the exact dynamics of a many channel scattering problem, the ES representation. Exact scattering solutions are derived in both time dependent and time independent frameworks for the representation and many interesting results in these frames are established. It is shown, e.g., that in a time dependent frame the usual Schrödinger propagator factorizes into internal Hamiltonian, ES, and energy correcting propagators. We also show that in a time independent frame the full Green's functions can be similarly factorize. Another important feature of the new representation is that it forms a firm foundation for seeking corrections to the ES approximation. Thus, for example, the singularity which arises in a conventional perturbative expansions of the full Green's functions (with the ES Green's function as the zeroth order solution) is avoided in the ES representation. Finally, a number of both time independent and time dependent ES correction schemes are suggested.