Examiner: 9014 University Lecturer Göran Wahnström
Computation is an integral part of modern science and the ability to exploit effectively the power offered by computers is therefore essential to a working physicist. The proper application of a computer to modeling physical systems is far more than blind number crunching, and the successful physicist draws on a balanced mixture of analytically soluble examples, physical intuition, and numerical work to solve problems that are otherwise intractable.
AIM OF SUBJECT
The course is aimed at refining computational skills by providing direct experience in using a computer to model physical systems.
CONTENT
Different numerical techniques will be applied to problems in classical, quantum and statistical physics. These problems will provide a vivid illustration of many basic and important concepts in theoretical physics. Special emphasis is directed to computer simulation methods, the Monte Carlo method and the molecular-dynamics technique, but also more traditional numerical methods will be included.
The different numerical techniques and the physical problems will be presented in a series of lectures. More specifically these will deal with: Solution of ordinary differential equations in classical mechanics, applied to non-linear dynamics and coupled anharmonic oscillators. The molecular-dynamics technique and various applications. Random-walk models, stochastic differential equations and Brownian dynamics. Monte Carlo integration, variance reduction, Markov chains and the Metropolis algorithm, with apllications to the Ising model, binary alloys, simple liquids, thermal expansion of solids, as well as path integrals in quantum mechanics. Solution of partial differential equations in quantum mechanics using short-time propagators, the finite difference methods and fast Fourier transform technique.
The most important part is, however, the students' own activity in applying and solving some of the problems using Unix-based workstations. This part will be integrated with computer laboratory work, where instructors will be available for consultation.
LITERATURE
The course will be based on lecture notes. The following will be used as reference literature:
W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling: Numerical Recipes, The Art of Scientific Computing, 2nd edition (Cambridge, 1992)
D.W. Heerman: Computer Simulation Methods in Theoretical Physics (Springer, 1990)
Steven E. Koonin and Dawn C. Meredith: Computational Physics (Addison Wesley, 1990)
EXAMINATION
The examination will be based on an oral and written presentation of problems solved by the student.
* Quantum Mechanics
* Condensed Matter Physics
* Statistical Physics
* Advanced Experimental Physics