9305582 Tomsovic Recent elegant experiments in mesoscopic, atomic and other systems are probing the deep connections between the quantum mechanical and classical mechanical worlds. The theory bridging the two worlds is the realm of semiclassical approximations for which many long-standing, fundamental problems remain unresolved. Although the bulk of the work on semiclassical mechanics has been concentrated in the energy domain, often the direct interest is in the time evolution of a system. Until very recently only very rudimentary time dependent semiclassical techniques existed. This work will focus on extending new, more powerful semiclassical propagation methods (which we developed) to apply to higher dimensions (which is important for physical applications), simplifying the problems arising from chaotic motion, investigating the leading corrections, and adapting the method to apply to stationary quantum mechanical problems. ! G 2 U F v F @ ~ F F ^ t 0 .u H F ~ u F H F v F . v v N Õ U v Õ F F x* v 0 = F t =/ t v v 0 =: t N F @ ^ S v Õ 8 6 8 ! ! A 8 8 ( Times New Roman Symbol & Arial " h ; % ; % / terri l. hicks terri l. hicks
