Multidimensional WKB approximation and the lifetime calculation - art. no.042101

Citation
J. Zamastil et al., Multidimensional WKB approximation and the lifetime calculation - art. no.042101, PHYS REV A, 6404(4), 2001, pp. 2101
Citations number
61
Categorie Soggetti
Physics
Journal title
PHYSICAL REVIEW A
ISSN journal
10502947 → ACNP
Volume
6404
Issue
4
Year of publication
2001
Database
ISI
SICI code
1050-2947(200110)6404:4<2101:MWAATL>2.0.ZU;2-E
Abstract
A Wentzel-Kramers-Brillouin (WKB) approach for calculating the lifetime of the ground state of two coupled oscillators with the most probable escape p ath along one of the coordinate axes is suggested. The WKB approximation of the wave function in the neighborhood of this path is obtained by scaling the corresponding variable. An analytic formula for the lifetime is derived and numerically verified. The method is applied to the Henon-Heiles potent ials. It is shown that the WKB method can be, in contrast to the numerical ones, easily extended to the problems of an arbitrary number of spatial dim ensions.