CLASSICAL HAMILTONIAN STRUCTURES IN WAVE-PACKET DYNAMICS

被引:69
作者
GRAY, SK [1 ]
VEROSKY, JM [1 ]
机构
[1] WESTERN WASHINGTON UNIV, DEPT MATH, BELLINGHAM, WA 98225 USA
关键词
D O I
10.1063/1.467219
中图分类号
O64 [物理化学(理论化学)、化学物理学];
学科分类号
070304 ; 081704 ;
摘要
The general, N state matrix representation of the time-dependent Schrodinger equation is equivalent to an N degree of freedom classical Hamiltonian system. We describe how classical mechanical methods and ideas can be applied towards understanding and modeling exact quantum dynamics. Two applications are presented. First, we illustrate how qualitative insights may be gained by treating the two state problem with a time-dependent coupling. In the case of periodic coupling, Poincare surfaces of section are used to view the quantum dynamics, and features such as the Floquet modes take on interesting interpretations. The second application illustrates computational implications by showing how Liouville's theorem, or more generally the symplectic nature of classical Hamiltonian dynamics, provides a new perspective for carrying out numerical wave packet propagation. We show how certain simple and explicit symplectic integrators can be used to numerically propagate wave packets. The approach is illustrated with an application to the problem of a diatomic molecule interacting with a laser, although it and related approaches may be useful for describing a variety of problems.
引用
收藏
页码:5011 / 5022
页数:12
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