The classical path approximation in time-dependent quantum collision theory

Stuart D. Augustin, Herschel Rabitz

Research output: Contribution to journalArticlepeer-review

52 Scopus citations


Time-dependent treatments of molecular collisions have frequently employed the combination of quantum equations for the internal degrees of freedom (i.e., vibration, rotation) with a classical description of the translational motion. In this paper, it is shown how energy-conserving classical path equations may be derived from first principles, thereby obtaining quantum correction terms of arbitrary order. These expressions have interesting implications for the question of how the classical limit is approached. If the translational degree of freedom is assumed to be described by a very narrow wave packet, the correction term to first order in ℏ is purely imaginary and therefore non-Hermitian. These techniques can be generalized to a classical treatment of other degrees of freedom, and the case of rotation in an atom-vibrotor collision is explicitly considered. For both the translational and rotational examples, the full series of corrections takes on an interesting and suggestive exponential form. The failure of classical path methods to satisfy microscopic reversibility is ascribed to a difficulty with the boundary conditions for the translational motion.

Original languageEnglish (US)
Pages (from-to)4195-4200
Number of pages6
JournalThe Journal of chemical physics
Issue number9
StatePublished - 1978

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy
  • Physical and Theoretical Chemistry


Dive into the research topics of 'The classical path approximation in time-dependent quantum collision theory'. Together they form a unique fingerprint.

Cite this