Exact scattering solutions in an energy sudden (ES) representation

Britton Chang, Larry Eno, Herschel Rabitz

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)4477-4485
Number of pages9
JournalThe Journal of chemical physics
Issue number7
StatePublished - 1983

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy
  • Physical and Theoretical Chemistry


Dive into the research topics of 'Exact scattering solutions in an energy sudden (ES) representation'. Together they form a unique fingerprint.

Cite this