Wavepacket path integral formulation of semiclassical dynamics

✍ Scribed by Eric J. Heller

• Publisher: Elsevier Science
• Year: 1975
• Tongue: English
• Weight: 500 KB
• Volume: 34
• Category: Article
• ISSN: 0009-2614
• DOI: 10.1016/0009-2614(75)85284-5

✦ Synopsis

The "quantum tmjectory" wavepacket approach to scmichssical collision dynamics is generalized to include effects which uuse distortion of inithlly gaussian wavepackets. The generalization takes the ion-n ol a discrete phn.zz space psth "integral" or sum. A complete set of gaussian phase space localized basis functions is proposed, and in the semiclassical limit, each basis function time develops in a simple cbssiul-like fashion. Thus, the fonnuhtion conveniently builds in the correct kniting semiclassical behavior. The phase space path sum is formally exact, numeriuUy it appears convcnicnt, nnd is apparently equally at home in quantum and semiclnssiczl re$mes.

Recently, a new quantum wavepacket trajectory approach to semiclassical dynamics has been developed

which attempts to exploit the simple behavior of localized gaussian wevepackets in the classical limit [I].

Delocalized quantum eigenstates are decomposed into time dependent iocalized packet states, each of which is propagated under an assumption that the potential may be quadratically expanded about the instantaneous center of each packet. Successfu! numerical ap-