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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 heavy-particle collisions, the inverse velocity is a large parameter; in single-domain ferromagnetism, thermal agitation (including Brownian motion and continuous-time random walks) is faced with a barrier of height 'sigma', a possibly large parameter. Methods of solution include phase-integral analysis, integral transforms and change-of-dependent variable. We shall consider the Schrödinger time-independent and time-dependent 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.
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- Verlag: Springer-Verlag GmbH
- Seitenzahl: 344
- Erscheinungstermin: 20. Dezember 2007
- ISBN-13: 9780387743134
- Artikelnr.: 37287581
"This book is based on some lectures given by the author to postgraduate Ph.D. students at the Centre for Atomic, Molecular and Optical Physics, School of Mathematics and Physics, of Queen's University Belfast, and reflects the author's research interests. ... At the end of the book, the reader will find a very rich list of references. The book is very instructive, both to physicists and mathematicians, in that it gives many important instances of the use of the fundamental technique of semiclassical approximation." (Alberto Parmeggiani, Mathematical Reviews, Issue 2011 d)