640-234 Further Classical & Quantum Mechanics

Physics 640-223 or 640-243.

Mathematics 620-231 or 620-233.

This subject is in two parts. Half of the subject deals with the powerful and elegant Lagrangian and Hamiltonian formulations of classical mechanics. As well as supplying new tools for problems in classical mechanics, these approaches also lead to deeper insights into the relationship between classical and quantum mechanics. Lagrangian dynamics is a valuable precursor to honours-level studies in theoretical physics. The other half of the subject deals with the further development of quantum mechanics, especially in relation to three-dimensional problems and the structure of matter.

Students completing this subject will be able to:

• explain the basic principles of the Lagrangian and Hamiltonian formulations of classical mechanics as well as the present-day microscopic picture of matter in terms of its basic constituents, ranging from atoms, molecules and solids to atomic nuclei and their constituent particles;

• apply Lagrangian and Hamiltonian techniques to the solution of some key problems in classical physics; and

• solve problems in quantum mechanics relevant to the hydrogen atom and other three-dimensional problems.

In addition students will enhance their ability to:

• participate effectively as part of a group in tutorials; and

• plan effective work schedules and manage their time to meet the deadlines for submission of assessable work and prepare for tests and examinations.

Topics include review of Newtonian mechanics; Lagrangian formulation: constraints, generalised coordinates, Lagrange's equations; Hamilton's variational principle; Hamiltonian formulation: conjugate momenta, Hamilton's equations, phase space, Poisson brackets; the Hamiltonian in quantum theory; spherical harmonics and angular momentum, hydrogen atom; introduction to many-electron atoms, Pauli Principle and intrinsic spin; and quantum statistical physics.

A 3-hour end-of-semester written examination; plus tests totalling up to two hours and/or projects and/or assignments totalling up to an equivalent of no more than 3000 words, set during the semester and which may account for up to 20% of the final mark.

• A P Arya, Introduction to Classical Mechanics. Allyn and Bacon.
• R A Serway, C J Moses and C A Moyer, Modern Physics. Saunders.