Dynamics by Semiclassical Methods

quantum approa ch. The evaluation of the quantum time evolution of a system requires the solution of the time-dependent Schr6dinger e:quation. A full numerical solution of the quantum problem is generally not feasible for cases involving more than a few degrees of freedom. The: situation is similar for the time-independent calculation of quantum transition probabilities in collision problems. Semiclassical methods build up approximate quantum solutions, which are numerically relatively easy to obtain, even for moderately long times, from information obtained along classical trajectories. Another reason for the attractiveness of semiclassical methods is their intuitive appeal. A semiclassical analysis of a problem allows the results to be interpreted in terms of classical trajectories, and this can provide a clearer picturc of the bchavior of the system than might be possible from quantum calculatio ns. Classical mechanics provides an accurate approximation of the dynamics of macroscopic systems, while quantum effects are very important on the microscopic lev el. Electronic states of atoms and molecules are known to be highly quantized, while the motion of molecules in a liquid are often well described by classical mechani cs. The scattering of molecules at rela