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.
The author is an expert in quantum dynamics and the processes of atomic collisions over 42 years and he has developed the mathematics of the semiclassical theory over 18 years and has applied this to condensed-matter physics. He is currently a Professor of Theoretical Physics in the Department of Applied Mathematics and Theoretical Physics at The Queen's University of Belfast. He has also been appointed Local Chair for the International Conference for Photonic, Electronic and Atomic Collisions in Belfast. Dr. Crothers other honors and memberships include:
Personal Chair in Theoretical Physics – Queens University (1985- )
Readership in Applied Mathematics and Theoretical Physics – Queen’s University (1976-1985)
Lecturer in Applied Mathematics – Queen’s University (1966-1976)
Fellow of American Physical Society (1994)
Fellow of Institute of Physics (1973)
Fellow of Institute of Mathematics and its Applications (1973)
Fellow of Institution of Electrical Engineers (1997)
Member of the Royal Irish Academy (1991)
Honorary Professor, Physics, St. Petersburg State University (2003)
Belfast Local Chair, ICPEAC XXVII, 2011 (2005)
Honorary Fellow, Trinity College Dublin (2006)