640-321 Quantum Mechanics (Advanced)

Credit Points

Coordinator

Prerequisites

Physics 640-223 or 640-243; Mathematics 620-231 and 620-232.

(For subjects completed prior to 1998, the Mathematics and Statistics departmental code 620- should be replaced by the superseded Mathematics departmental code 618-)

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 1-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.

Assessment

A 2.5-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

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