Condensed-matter physics plays an ever increasing role in photonics, electronic and atomic collisions research. Dispersion (Dynamics and Relaxation) includes scattering/collisions in the gaseous phase. It also includes thermal agitation, tunneling and relaxation in the liquid and solid phases. Classical mechanics, classical statistical mechanics, classical relativity and quantum mechanics are all implicated. 'Semiclassical' essentially means that there is a large or asymptotic real parameter. 'Semiclassical' can also mean 'classical with first-order quantal correction', based on an exponentiated Liouville series commencing with a simple pole in the -plane, being Planck's reduced constant and coming with all the attendant connection problems associated with the singularity at the turning or transition point and with the Stokes phenomenon. Equally,' semiclassical' can mean 'electrons described quantally and the heavy particles classically'. This latter gives rise to the so-called impact parameter method based on a pre-assigned classical trajectory.