Teaching
Here I have collected some teaching materials for the physics modules I lecture at UCD, including links to my online video content.Online video lectures on my YouTube channel
Check out my YouTube channel online and Subscribe to get notifications of new online content! Classical Mechanics and Relativity
These lectures are part of the UCD physics module PHYC30020 (3rd year undergraduate, semester 1). The
YouTube playlist organizes the lectures in order.
- Introduction and recap of Newtonian mechanics
- The Principle of Least Action
- Euler-Lagrange and Hamilton's equations
- Relativistic Lagrangian and Electromagnetism
- Derivation of classical physics from quantum mechanics
- Coordinate transformations and the metric of space
- Generalized coordinates and constraints in Lagrangian mechanics
- Conservation laws and Noether's theorem
- Worked examples in classical Lagrangian mechanics
- Chaos and Ergodicity
- Classical Hamiltonian mechanics and Energy
- Phase space trajectories
- Poisson Brackets and Canonical Transformations
- Introduction to Relativity
- Derivation of Lorentz transformation
- Relativistic length contraction and time dilation
- Paradoxes in Special Relativity
- Relativistic Velocity Addition
- Relativistic Invariants
- Causality in Special Relativity
- Four-Vectors in special relativity
- Relativistic Mechanics
Quantum Condensed Matter Theory
These lectures are part of the UCD physics module PHYC40200 (4th year undergraduate / MSc, semester 2).
The
YouTube playlist organizes the lectures in order.
- Quantum Condensed Matter Physics lectures: orientation
- Intro to Quantum Condensed Matter Physics
- Quantum harmonic oscillator and ladder operators for spin systems
- Two qubits / spins: formalism
- Spin states and exchange interaction
- Exact Diagonalization for spin systems
- Observables, Density Matrix, Reduced Density Matrix, Entanglement Entropy
- Spin chains and the quantum to classical correspondence
- Spin wave theory of ferromagnets and Holstein Primakoff representation
- phase transitions, spontaneous symmetry breaking, and mean field theory
- Quantum spin liquids and valence bond solids
- Second quantization: basics
- Second quantization for fermions
- Basic fermionic models in second quantized form
- Tight-binding models
- Fundamentals of band structure
- Electron interactions and the Hubbard model
- Topological quantum matter
- Green's functions in condensed matter physics: basics
- Green's functions for non-interacting systems
- Equations of motion for Green's functions in CMP
- Green's functions for interacting fermions
Electromagnetism
These lectures are part of the UCD physics module PHYC30070 (3rd year undergraduate, semester 2). The YouTube playlist organizes the lectures in order.
- Magnetostatics
- Magnetic materials and magnetic fields in matter
- Electrodynamics and Faraday's law
- Energy in electrodynamic systems
- Electromagnetic waves
- Electrodynamic potentials
- Relativity in Electrodynamics
Classical Mechanics and Relativity (PHYC30020)
UCD 3rd year undergraduate physics: Semester 1
The first part of this module covers non-relativistic classical mechanics with applications: generalised coordinates, degrees of freedom, Lagrange's formalism and Lagrange's equations of motion, Hamilton's principle and Hamilton's equation of motion, central force motion, continuous systems and fields. The second part of this module covers special relativity with applications in particle and astrophysics: Michelson-Morley experiment, Einstein's postulates, Lorentz transformations, time dilation and length contraction, relativity of simultaneity, four-vector formalism, relativistic energy-momentum-mass relationship, and relativistic imaging.
Electromagnetism (PHYC30070)
UCD 3rd year undergraduate physics: Semester 2
This module presents the field theory of electromagnetism. Gauss's Law, Ampere's Law, Biot-Savart's Law and Faraday's Law are examined, leading to Maxwell's Equations. The physical significance of these equations is emphasised. Solutions to Maxwell's Equations in the form of electromagnetic waves are presented. The behaviour of electromagnetic fields in vacuum, dielectric and magnetic media, conductors, wave-guides, and at the interface between different media is described. Electromagnetism as a relativistic phenomenon is discussed and the nature of light is investigated. The source of electromagnetic radiation is identified.
Quantum Theory of Condensed Matter (PHYC40200)
UCD 4th year undergraduate physics: Semester 2
This module will introduce methods of many-body quantum mechanics, as applied to condensed matter physics. The fundamental formalism and techniques are presented, with examples of applications to relevant physical systems. Topics covered include second quantization, spin systems and magnetism, quantum gases, tight-binding models, strongly correlated electrons, scattering theory, Green's functions, topological quantum matter, quantum transport (subject to change).
Theoretical Physics Projects (PHYC40900)
UCD 4th year undergraduate theoretical physics Bachelor's thesis: Semesters 1 & 2
This module involves an extended original research project in theoretical physics, with topics including but not restricted to: General Relativity Theory, Theoretical Astrophysics, and Condensed Matter Theory. Based on original research articles, the student will explore a current research topic of his/her choice selected from a list proposed by the module co-ordinator, and will be supported by an appropriate supervisor. The student will summarize his/her findings in a written report and an oral presentation.
Previous courses in UCD:
Advanced Lab - computational physics (PHYC303XX)
UCD 3rd year undergraduate physics: Semesters 1 & 2, 2017/18
Principles of Scientific Enquiry (PHYC10010)
UCD 1st year undergraduate science: Semester 1, 2016-19
Courses outside UCD:
Numerical methods for quantum impurity problems
Part of the Dutch Research School of Theoretical Physics (DRSTP)Doorn, Netherlands (9-20th March 2015)
Course Summary:
'Quantum impurity models' are classic paradigms for strong electron correlations in condensed matter physics. They underpin the theoretical description of magnetic impurities in metals, nanodevices such as quantum dots, and appear as effective models within the dynamical mean field theory of correlated materials. Non-perturbative quantum many-body methods must be employed to solve such problems. In this course, we provide the conceptual framework of the Numerical Renormalization Group, discuss technical/practical details of the calculation, and present relevant applications.
Visit the 'Quantum impurity' course website
Numerical Methods for Many-Particle Systems (Graduate)
Held at the Institute for Theoretical Physics, University of Cologne, Germany.In conjunction with the Bonn-Cologne Graduate School of Physics and Astronomy.
Course Summary:
This intensive course is intended to provide both a working understanding and real hands-on experience with the essential numerical techniques of solid state many-body physics. Rather than a 'black-box' philosophy, the course aims to discuss the theory and physics underpinning numerical approaches. Lectures will introduce models of central importance, such as the Ising model, the Anderson impurity model, the Hubbard model and the Heisenberg model. Using these as concrete examples, the Monte Carlo, Exact Diagonalization, Numerical Renormalization Group and Density Matrix Renormalization Group techniques will be discussed. Students will also gain supervised practical hands-on experience writing, using and modifying simple computer codes to solve real problems.
Numerical Renormalization Group (Graduate)
Held at the Department of Theoretical Physics, University of Gothenburg, Sweden.Course Summary:
'Quantum Impurity Problems' are classic paradigms for strong electron correlations in condensed matter physics. They underpin the theoretical description of magnetic impurities in metals, nanodevices such as quantum dots, and appear as effective models within the dynamical mean field theory of correlated materials. Non-perturbative quantum many-body methods must be employed to solve such problems. In this course, we provide the conceptual framework of the Numerical Renormalization Group, discuss technical/practical details of the calculation, and present relevant applications.
Mathematics (Undergraduate)
Held at Oxford University, UK.Course Summary:
Designed to provide the foundational and advanced mathematics required in physical chemistry and beyond, this course comprises weekly lectures and classes throughout the first year of the Undergraduate chemistry degree at Oxford University.