640-321 Quantum Mechanics (Adv)

Physics 640-223 or 640-243; mathematics 620-231 or 620-233; and mathematics 620-232 or 620-234

Quantum mechanics plays a central role in our understanding of fundamental phenomena primarily in the microscopic domain. It lays the foundation for an understanding of atomic, molecular, condensed matter, nuclear and particle physics.

Students completing this subject will be able to:

• explain important concepts in quantum physics including the probability interpretation, the Heisenberg uncertainty principle, conservation laws and spin;

• solve problems applying quantum mechanical theory to situations involving atoms, molecules, solids, nuclei and elementary particles; and

• analyse solutions to predict measurable quantities.

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 covered include the probability interpretation, time evolution and the Schrödinger equation, Fourier transforms, Hermitian operators, the eigenvalue problem, expectation values, the Heisenberg uncertainty principle and commutation relations, symmetries and conservation laws, the Dirac delta-function. The quantum mechanics of angular momentum is developed and then applied to central force systems such as the hydrogen atom. The energy eigenstates of the one-dimensional harmonic oscillator are also analysed. The physics of spin-1/2 particles is developed using the matrix theory of spin. The Hilbert space or state vector formulation of quantum mechanics is developed and Dirac bra-ket notation introduced. Time-independent perturbation theory is introduced.

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.

• B H Bransden and C J Joachain, Introduction to Quantum Mechanics. Longmans.
  or
  E Merzbacher, Quantum Mechanics. Wiley.