640-321 Quantum Mechanics (Adv)

Credit Points

HECS Band

Coordinator

Prerequisites

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

Semester

Contact

Subject Description

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, solid-state, nuclear and particle physics. By the completion of this subject the student should have a thorough grounding in the principles of quantum mechanics as they relate to both wave-mechanical and spin systems. 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.

Assessment

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 mark.

Prescribed Texts

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