This repository contains a collection of my handwritten notes from my Third Year in Physics (BSc) at Durham University. These notes aim to provide a detailed and accessible resource for key topics covered and I hope they prove valuable to other students on the same or related courses and serve as a useful revision aid!
| Key Concepts | |
|---|---|
| Many-particle systems (wave functions, identical particles, bosons, fermions, Slater determinant) | Variational method (ground state, excited states, trial functions with linear variational parameters) |
| Ground state of two-electron atoms | Excited states of two-electron atoms (singlet and triplet states, exchange splitting, exchange interaction) |
| Complex atoms (electronic shells, central-field approximation) | Time-dependent perturbation theory, Fermi's Golden Rule, periodic perturbations |
| Schrödinger equation for charged particle in an electromagnetic field | Dipole approximation, transition rates for harmonic perturbations |
| Absorption and stimulated emission, Einstein coefficients | Spontaneous emission, selection rules for electric dipole transitions, lifetimes |
| Interaction of particles with a static magnetic field (spin and magnetic moment) | Particle of spin one-half in a uniform magnetic field, charged particles with uniform magnetic fields |
| Larmor frequency, Landau levels | One-electron atoms in magnetic fields |
| Key Concepts | |
|---|---|
| Fundamental Interactions, symmetries and conservation Laws | Global properties of nuclei (nuclides, binding energies) |
| Semi-empirical mass formula, the liquid drop model | Charge independence and isospin |
| Nuclear stability and decay (beta-decay, alpha-decay, nuclear fission, decay of excited states) | The nuclear force (nucleon-nucleon scattering, the deuteron, the nuclear force) |
| The structure of nuclei (Fermi gas model, shell Model, predictions of the shell model) |
| Key Concepts | |
|---|---|
| Scattering (relativistic kinematics, elastic and inelastic scattering, cross sections, Fermi's golden rule, Feynman diagrams) | Geometric shapes of nuclei (kinematics, Rutherford cross section, Mott cross section, nuclear form factors) |
| Elastic scattering off nucleons (nucleon form factors) | Deep inelastic scattering (nucleon excited states, structure functions, the parton model) |
| Quarks, gluons, and the strong interaction (quark structure of nucleons, quarks in hadrons) | Particle production in electron-positron collisions (lepton pair production, resonances) |
| Phenomenology of the weak interaction (weak interactions, families of quarks and leptons, parity violation) | Exchange bosons of the weak interaction (real W and Z bosons) |
| The Standard Model | Quarkonia (analogy with Hydrogen atom and positronium, Charmonium, quark-antiquark potential) |
| Hadrons made from light quarks (mesonic multiplets, baryonic multiplets, masses and decays) |
| Key Concepts | |
|---|---|
| Review of the effect of a periodic potential, energy gap | Reduced and periodic zone schemes |
| Semiconductor crystals: crystal structures, band gaps | Equations of motion, carrier concentrations of intrinsic and extrinsic semiconductors |
| Law of mass action, transport properties | p-n junction |
| Superconductivity: Meissner effect, London equation | Type I and type II superconductors, thermodynamics of superconductors |
| Landau-Ginzburg theory, Josephson junctions | Diamagnetism and paramagnetism: Langevin equation |
| Quantum theory of paramagnetism, Hund's rules, crystal field splitting | Paramagnetism of conduction electrons |
| Ferromagnetism and antiferromagnetism: Curie point, exchange integral, magnons | Antiferromagnetism, magnetic susceptibility |
| Dielectrics and ferroelectrics: macroscopic and local electric fields | Dielectric constant and polarizability, structural phase transitions |
| Key Concepts | |
|---|---|
| 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 |
| Key Concepts | |
|---|---|
| Overview of the Solar System | Orbital dynamics |
| Planetary interiors | Planetary atmospheres |
| Formation of the Solar System | Extrasolar planets |
| Key Concepts | |
|---|---|
| Observational overview and the expansion of the Universe | The cosmological principle (homogeneity and isotropy) |
| Newtonian gravity and the Friedmann equation | The geometry of the Universe |
| Solutions of Friedmann's equations | The age of the Universe |
| Weighing the Universe (dark matter, dark energy) | The cosmological constant |
| General relativistic cosmology (the metric and Einstein equations) | Classic cosmology (distances and luminosities) |
| Type Ia SNe and galaxy number counts | The cosmic microwave background |
| The thermal history of the Universe | Primordial nucleosynthesis |
| Dark matter | Problems with the hot big bang |
| Inflation | Current constraints on cosmological parameters |
| Key Concepts | |
|---|---|
| Calculus of Variations: Euler—Lagrange equations | Classic variational problems |
| Lagrange multipliers | Infinite series and convergence |
| Asymptotic series | Integration, Gaussian and related integrals |
| Gamma function |
| Key Concepts | |
|---|---|
| Functions of complex variables | Differentiable functions, Cauchy-Riemann conditions |
| Harmonic functions | Multiple valued functions and Riemann surfaces |
| Branch points and cuts | Complex integration, Cauchy's theorem |
| Taylor and Laurent series | Poles and residues, residue theorem and definite integrals |
| Residue theorem and series summation |
| Key Concepts | |
|---|---|
| Vectors and matrices | Hilbert spaces |
| Linear operators | Matrices |
| Eigenvalue problem | Diagonalisation of matrices |
| Co-ordinate transformations | Tensor calculus |
| Key Concepts | |
|---|---|
| Fourier series and transforms | Convolution theorem |
| Parseval's relation | Wiener-Khinchin theorem |
| Momentum representation in quantum mechanics | Hilbert transform |
| Sampling theorem | Laplace transform, inverse Laplace transform and Bromwich integral |
These notes are licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
See LICENSE file for more detail.
These notes were originally created during my personal study in 2023/24 and are not official course materials. While every effort has been made to ensure accuracy, they are not being updated to reflect changes to the curriculum and I cannot guarantee the content is free from errors. I recommend using them alongside the materials provided and recommened by your lecturers.
If you have any questions, spot mistakes, or want to contribute to the repository, feel free to:
- Open an issue on the GitHub Issues page.
- Reach out to me directly via email.
- Clone the repository and submit a pull request — all constructive input is welcome!