Semiclassical dynamics and relaxation (Q924186)

The book under review is based on some special lectures given by the author to postgraduate PhD students in the Center for Atomic, Molecular and Optical Physics in the School of Mathematics and Physics, Queen's University Belfast, in May and June 2003. In short, the first chapter is a brief review of some notions of applied mathematics which will be used further. Chapters 2-4 concern with atomic and molecular physics in the gaseous phase. Chapter 5 describes the field of condensed matter physics in the liquid and solid phases. Chapter one, Mathematics for the semiclassicist, starts recalling the properties of an analytic function. The steepest descent and asymptotic methods in numerical analysis are described followed by a review of perturbation theories, hypergeometric series, combinatorics, generalized hypergeometric functions and Fourier and Laplace transforms. Moreover, in order to introduce the Stokes phenomenon for example, are described contour integral transforms. Chapter two, Semiclassical Phase Integrals, describes the semiclassical approximation also known as JWKB (or WKB) approximation (because it was first developed in quantum mechanics by Jeffreys, Wentzel, Kramers and Brillouin) with applications to coupled wave equations. The Stokes phenomenon with one transition point is presented. More, in the next sections one finds the extension to 2--4 transition points and other generalizations to four close curve-crossing translation points. If the Chapter 2 can be considered the one-dimensional semiclassical JWKB Approximation, in Chapter 3, Semiclassical method for hyperspherical coordinate systems, contains the generalization to higher dimensions by way of Wannier's classical treatment of electron correlation. Chapter 4, Ion-atom collisions, describes another meaning of semiclassical, different from the one from Chapters 2 and 3, concerning here an ion-atom collision in which the relative motion of the two nuclei is treated classically while the motion of one or more electrons is treated fully quantally. The continuum-distorted-wave (CDW), another dynamic molecular theory and some generalizations are presented. This chapter ends with the description of the semiclassical acausality. The last chapter, Diffusion in liquids and solids, is concerned with the condensed-matter physics in the liquid and solid phases. First are discussed single-domain ferromagnetic particles and then the dielectric relaxation is treated. The References include 614 titles of books and articles representing an ample source of information for further studies.