Semiclassical dynamics and relaxation
 Author/Creator
 Crothers, Derrick S. F.
 Language
 English.
 Imprint
 New York : Springer, c2008.
 Physical description
 xi, 342 p. : ill. ; 24 cm.
 Series
 Springer series on atomic, optical, and plasma physics ; 47.
Access
Available online
 site.ebrary.com ebrary
 dx.doi.org SpringerLink

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QC20 .C76 2008

Unknown
QC20 .C76 2008
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Contents/Summary
 Bibliography
 Includes bibliographical references (p. [321]335) and index.
 Contents

 Mathematics for the Semiclassicist. Semiclassical Phase Integral. Semiclassical Methods for Hyperspherical Coordinate Systems. IonAtom Collisions. Diffusion in Liquids and Solids. Continued Fraction Solutions of Eq. (5.301). MittagLeffler Fuctions. Nonlinear Response to Alternating Fields. References. Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 Condensedmatter 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 firstorder 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 socalled impact parameter method based on a preassigned classical trajectory. With evermore sophisticated experiments, it has become equally more important to test theory over a wider range of parameters. For instance, at low impact energies in heavyparticle collisions, the inverse velocity is a large parameter; in singledomain ferromagnetism, thermal agitation (including Brownian motion and continuoustime random walks) is faced with a barrier of height 'sigma', a possibly large parameter. Methods of solution include phaseintegral analysis, integral transforms and changeofdependent variable. We shall consider the Schrodinger timeindependent and timedependent equations, the Dirac equation, the Fokker Planck equation, the Langevin equation and the equations of Einstein's classical general relativity equations. There is an increasing tendency among physicists to decry applied mathematics and theoretical physics in favour of computational blackboxes. One may say applied mathematics concerns hard sums and products (and their inverses) but unless one can simplify and sum infinite series of products of infinite series, can one believe the results of a computer program? The era of the polymath has passed; this book proposal aims to show the relevance to, and impact of theory on, laboratory scientists.
(source: Nielsen Book Data)
Bibliographic information
 Publication date
 2008
 Responsibility
 D.S.F. Crothers.
 Series
 Springer series on atomic, optical, and plasma physics ; 47
 Note
 " ... based on a set of five special lectures given to postgraduate PhD students in the Centre for Atomic, Molecular and Optical Physics, in the School of Mathematics and Physics, Queen's University Belfast, in May and June 2003"Pref.
 ISBN
 9780387743127
 038774312X
 9780387743134
 0387743138