This course unit is intended primarily for Mathematical Physics SH students but it may be attended - either seriously or on a `sitting in' basis - by Physics SH and Astrophysics SH students, graduate students, and indeed by anyone else interested in understanding nonrelativistic and relativistic quantum theory. Prior attendence at the third year courses on Quantum Mechanics, Lagrangian Dynamics and Complex Analysis, and the fourth year course on Quantum Physics, is strongly recommended. Relativistic Electromagnetism and Advanced Mathematical Methods would also be useful. Students are warned that there will be no printed lecture notes: come to the lectures and make your own!
Historically quantum mechanics began with two quite different mathematical formulations: the wave equation of Schroedinger, and the matrix algebra of Heisenberg. While these approaches are well suited to the nonrelativistic bound state problems of atomic and molecular physics, many problems in condensed matter and particle physics are better suited to a more intuitive formulation of quantum mechanics based on the ideas of Dirac and Feynman: the path integral or "sum over histories" approach. In this course we will review the fundamental ideas of quantum mechanics, introduce the path integral for a nonrelativistic point particle, and use it to derive time dependent perturbation theory and the Born series for nonrelativistic scattering. The course concludes with a brief introduction to relativistic quantum mechanics and the ideas of quantum field theory.
As a stimulating introduction to the course:
The following textbooks are closest to the level of course itself:
Problem solving is the best way to learn and understand mathematical physics. For this course there will be eight problems classes at which solutions to the more difficult problems will be presented on the blackboard as required. I will also be available in my office to answer any remaining questions about the lectures and the associated problem sheets.
Students are warned that no written solutions will be provided to the problems. It is thus essential that each student intending to take the course seriously makes a determined attempt to construct their own solutions to the problems BEFORE the appropriate problems class, so that any difficulties he or she finds during the course of solving the problems may be resolved during the class.
Back to RDB home page, or the departmental internal page.
R.D. Ball
September 2006