PHYS3631 Foundations of Physics 3B (2012/13)
18 lectures + 3 examples classes in Michaelmas Term
- Review of EM [Hecht Section 2.8, 3.2 and Appendix 1]
- Plane waves and spherical waves [Hecht Section 2.7 and 2.9]
- Fourier transforms: Linearity, convolution, shifting, scaling [Hecht Chapter 11]
- Propagating the solution to the wave equation using the angular spectral method [Goodman Chapter 3]
- Gaussian beams [Hecht Section 13.1]
- Near-field (Fresnel) and far-field (Fraunhofer) diffraction [Hecht Section 10.1 and 10.3]
- Simple cases: single and double slits [Hecht Section 10.1 and 10.2]
- Simple cases: multiple slits [Hecht Section 10.1 and 10.2]
- Phasors [Hecht Section 4.5 and 4.11]
- 2D diffraction: letters, and circular apertures [Hecht Section 10.2.3 and 10.3]
- Diffraction limit: Rayleigh criterion, Heisenberg microscope [Hecht Section 10.2]
- Spatial filtering [Hecht Section 13.2]
- Babinet’s Principle. Apodization [Hecht Section 10.3]
- Fabry Perot: Gaussian modes of a cavity [Hecht Section 9.6 and 13.1]
- Lasers and cavities [Hecht Section 13.1]
18 lectures + 3 examples classes in Michaelmas and Epiphany Term
Syllabus: Introduction and basic ideas:- macro and microstates, distributions; distinguishable particles, thermal equilibrium, temperature, the Boltzmann distribution, partition functions, examples of Boltzmann statistics: spin-1/2 solid and localized harmonic oscillators; Gases: the density of states: fitting waves into boxes, the distributions, fermions and bosons, counting particles, microstates and statistical weights; Maxwell-Boltzmann gases: distribution of speeds, connection to classical thermodynamics; diatomic gases: Energy contributions, heat capacity of a diatomic gas, hydrogen; Fermi-Dirac gases: properties, application to metals and helium-3; Bose-Einstein gases: properties, application to helium-4, phoney bosons; entropy and disorder, vacancies in solids; phase transitions: types, ferromagnetism of a spin-1/2 solid, real ferromagnetic materials, order-disorder transformations in alloys; statics or dynamics? ensembles, chemical thermodynamics: revisiting chemical potential, the grand canonical ensemble, ideal and mixed gases; dealing with interactions: electrons in metals, liquid helium 3 and 4, real imperfect gases; statistics under extreme conditions: superfluid states in Fermi-Dirac systems, statics in astrophysical systems.
12 lectures + 2 examples classes in Epiphany Term
Syllabus: paramagnetism, mean field theory, ferromagnetism, antiferromagnetism, Curie-Weiss law, magnetic excitations, bulk magnetic properties, domains walls, magnetostriction, magnetic order and exchange interaction, Heisenberg hamiltonian. Critical temperature and field, London equation, type I and type II superconductors, vortex states, flux pinning.
3 lectures in Easter Term, one by each lecturer
Lectures: 2 or 3 one-hour lectures per week.
Examples classes: These provide an opportunity to work through and digest the course material by attempting exercises and assignments assisted by direct interaction with the lecturers and demonstrators. Students will be divided into groups, each of which will attend one one-hour class every week.
Problem exercises: See http://www.dur.ac.uk/physics/students/problems/