Classical, Quantal and Semiclassical Propagators and Applications to Elastic Scattering

Semiclassical methods predate even full quantum mechanics starting with Bohr's atom model. Semiclassical propagators have been developed continuously in chemical physics ever since Miller's seminal classical S-matrix. Semiclassics was revived with the success of periodic orbit quantization and chaotic dynamics entering the quantum domain. Today, semiclassical and even classical concepts are accepted to describe microscopic phenomena, from protein folding over plasma physics all the way to atoms in strong laser fields. Thereby, semiclassical approximations are used for computation as well as for physical insight. Explicit formulae are given for elastic scattering, always covering quantum, classical, and semiclassical expressions.