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. Topics include review of Newtonian mechanics; Lagrangian formulation: constraints, generalised coordinates, Lagrange's equations; Hamilton's variational principle, the action; selected applications; Hamiltonian formulation: conjugate momenta, Hamilton's equations, phase space, Poisson brackets; and the Hamiltonian in quantum theory. 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. Topics include 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 and/or assignments, set during the semester, which may account for up to 20% of the final marks.

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