Path integral derivations of novel complex trajectory methods

Details Path integral derivations of novel complex trajectory methods Path integral derivations of novel complex trajectory methods

2008-07-29

arxiv.org/abs/0807.4659v2

Physics

Quantum Physics

41 pages; references and citations were corrupted in first two versions, sorry

Scientific paper

Path integral derivations are presented for two recently developed complex trajectory techniques for the propagation of wave packets, Complex WKB and BOMCA. Complex WKB is derived using a standard saddle point approximation of the path integral, but taking into account the hbar dependence of both the amplitude and the phase of the intial wave function, thus giving rise to the need for complex classical trajectories. BOMCA is derived using a modification of the saddle point technique, in which the path integral is approximated by expanding around a near-classical path, chosen so that up to some predetermined order there is no need to add any correction terms to the leading order approximation. Both Complex WKB and BOMCA give the same leading order approximation; in Complex WKB higher accuracy is achieved by adding correction terms, while in BOMCA no additional terms are ever added -higher accuracy is achieved by changing the path along which the original approximation is computed. The path integral derivation of the methods explains the need to incorporate contributions from more than one trajectory, as observed in previous numerical work. On the other hand, it emerges that the methods provide efficient schemes for computing the higher order terms in the asymptotic evaluation of path integrals. The understanding we develop of BOMCA suggests that there should exist near-classical trajectories that give exact quantum dynamical results when used in the computation of the path integral keeping just the leading order term. We also apply our path integral techniques to give a compact derivation of the semiclassical approximation to the coherent state propagator.

Affiliated with

Also associated with

No associations

Rating

Path integral derivations of novel complex trajectory methods does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Path integral derivations of novel complex trajectory methods, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Path integral derivations of novel complex trajectory methods will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-38807