Pre-requisites
Familiarity with the following concepts and techniques is highly
recommended.
- Advanced Classical Physics (Level 3 option)
is a pre-requisite to this course.
Familiarity with the following topics will be useful:
- Hamiltonian mechanics: normal modes.
- Hamiltonian for motion in a magnetic field: momentum and use of vector potential.
- Concepts in Quantum Mechanics (Level 2 core)
- Heisenberg uncertainty principle
- Hamiltonians and Schrodinger's equation
- Simple harmonic oscillator: energy levels, ladder operators.
(We will revise this briefly during the course.)
- Quantum statistics: Bose-Einstein distribution, Fermi-Dirac distribution.
See Statistical Physics (Level 2 core).
- Electrons in Solids (Level 2 core).
- Free electron theory: electron Fermi surface, Fermi energy
- Density of states
- Electromagnetism (Level 2 core)
- Magnetic flux
- Maxwell's equations: Faraday's law
- Mathematics
- Fourier series and Fourier transforms. See Level 2 core
Mathematics
- Calculus of variation: Euler-Lagrange equation. See Level 2 option: Mathematical Methods
Overlap with other courses
This course covers concepts in physics which are also discussed
in other option courses.
- Statistical Mechanics
- Landau theory of phase transitions
- Quantum Field Theory
This course
contains applications of quantum fields in condensed matter physics.
- creation and annihilation operators
- second quantisation