| Unit name | Quantum Physics 301 |
|---|---|
| Unit code | PHYS32011 |
| Credit points | 10 |
| Level of study | H/6 |
| Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
| Unit director | Professor. Hayden |
| Open unit status | Not open |
| Pre-requisites |
120 credit points at Level 5 in Physics, Physics with Astrophysics, joint honours in Mathematics and Physics or Physics and Philosophy, or Chemical Physics programmes. |
| Co-requisites |
None |
| School/department | School of Physics |
| Faculty | Faculty of Science |
Dirac's formulation of Quantum Mechanics. Brief review, using Dirac notation, of complex linear vector spaces, operators, eigenvalues and eigenvectors. Postulates of quantum mechanics, the measurement process. Operators with continuous spectra of eigenvalues and eigenvectors. Connection with the wave-mechanical formulation of quantum mechanics. Position and momentum representations of the wave-function. Solution of the harmonic oscillator using ladder operators as an illustration of operator methods. Angular momentum operators: raising and lowering operators. Pauli matrices and electron spin. Addition of angular momentum. Spin singlet and triplet states of two spin particles. Spin orbit interactions and atomic fine structure. Hyperfine structure and Lamb shift (briefly). Perturbation theory (time-independent) in the non-degenerate case. Examples: the perturbed harmonic oscillator and the induced electric dipole moment of an atom. Second-order perturbation theory. Perturbation theory in the degenerate case. Example: the Stark effect in excited states of the hydrogen atom. Time-dependence. An example: two-state systems. The Schrödinger and Heisenberg equations of motion. Time-dependent perturbation theory. Fermi's Golden Rule. Example: electromagnetic transitions in atoms. Selection rules and forbidden transitions. Absorption, stimulated and spontaneous emission.This is a pre-requisite for the Level 7 Advanced Quantum Mechanics unit.
Aims:
To introduce students to the balance of quantum mechanics appropriate to level 6 comprising operator formalism in quantum mechanics, Dirac notation, perturbation theory.
Understand and use the operator formalism or quantum mechanics to solve the harmonic oscillator. Have a basic knowledge of the foundations of quantum mechanics and the importance of operators and state vectors. Able to apply first and second order perturbation theory to a number of simple models. Able to use time-dependent perturbation theory in simple cases and calculate the transition probability for simple potentials.
Lectures, problems classes
Written examination comprising 1 2-hour paper
