Theoretical Physicist Course

Lesson 1 • Ordinary Differential Equations

Develops solution techniques for ODEs governing physical motion and fields. Connects directly to Newton's laws and oscillatory systems.

Lesson 2 • Partial Differential Equations

Covers wave, heat, and Laplace equations central to classical and quantum physics. Separation of variables and Green's functions are emphasized.

Lesson 3 • Complex Analysis and Special Functions

Introduces complex variables, contour integration, and special functions used throughout physics. Residue theorem enables evaluation of physical integrals.

Lesson 4 • Linear Algebra and Tensor Calculus

Introduces vector spaces, matrices, eigenvalue problems, and tensors. Tensors are essential for relativity and continuum mechanics.

Lesson 1 • Hamiltonian Mechanics

Reformulates mechanics using phase space and Hamilton's equations. Canonical transformations and Poisson brackets prepare students for quantum mechanics.

Lesson 2 • Small Oscillations and Normal Modes

Treats coupled oscillators and normal mode decomposition using matrix methods. Lays groundwork for field quantisation and phonon physics.

Lesson 3 • Lagrangian Mechanics

Introduces generalised coordinates and the principle of least action. Euler-Lagrange equations replace Newton's laws in complex systems.

Lesson 4 • Newtonian Mechanics and Conservation Laws

Reviews Newton's laws and derives conservation of energy, momentum, and angular momentum. Provides the physical intuition underlying formal mechanics.

Lesson 1 • Electrostatics and Magnetostatics

Derives Coulomb's law, Gauss's law, and Biot-Savart law from Maxwell's equations. Establishes field concepts and potential theory for static configurations.

Lesson 2 • Electromagnetic Potentials and Gauge Theory

Introduces scalar and vector potentials and gauge freedom. Lorentz and Coulomb gauges are applied to simplify field equations.

Lesson 3 • Maxwell's Equations and Electromagnetic Waves

Presents the full set of Maxwell's equations and derives the wave equation. Plane wave solutions and polarisation states are analysed in detail.

Lesson 4 • Radiation from Accelerating Charges

Derives Lienard-Wiechert potentials and radiation fields from moving charges. Larmor formula and synchrotron radiation are key outcomes.

Lesson 1 • Special Relativity and Spacetime

Introduces Lorentz transformations, four-vectors, and spacetime intervals. Resolves apparent paradoxes and establishes covariant notation.

Lesson 2 • Differential Geometry for Gravity

Introduces manifolds, metric tensors, Christoffel symbols, and curvature tensors. These geometric tools are prerequisites for general relativity.

Lesson 3 • Covariant Electrodynamics

Reformulates Maxwell's equations using four-tensors and the electromagnetic field tensor. Demonstrates manifest Lorentz covariance of electrodynamics.

Lesson 4 • Solutions and Physical Applications

Analyses Schwarzschild and Friedmann-Robertson-Walker solutions. Covers black holes, gravitational waves, and standard cosmological models.

Lesson 1 • Schrödinger Equation and Canonical Problems

Derives the time-dependent and time-independent Schrödinger equations. Solves the infinite well, harmonic oscillator, and hydrogen atom exactly.

Lesson 2 • Angular Momentum and Spin

Develops angular momentum algebra using ladder operators and Clebsch-Gordan coefficients. Introduces intrinsic spin and its physical consequences.

Lesson 3 • Hilbert Space and Dirac Formalism

Introduces state vectors, operators, and the Dirac bra-ket notation. Establishes the mathematical framework for all subsequent quantum theory.

Lesson 4 • Approximation Methods

Covers time-independent and time-dependent perturbation theory, variational method, and WKB approximation. Applies these to atomic and molecular systems.

Lesson 1 • Thermodynamic Foundations

Reviews laws of thermodynamics, thermodynamic potentials, and Maxwell relations. Establishes the macroscopic framework that statistical mechanics must reproduce.

Lesson 2 • Statistical Ensembles

Introduces microcanonical, canonical, and grand canonical ensembles. Derives partition functions and connects them to free energies.

Lesson 3 • Quantum Statistical Mechanics

Applies statistical mechanics to quantum systems obeying Fermi-Dirac and Bose-Einstein distributions. Treats ideal quantum gases and their physical realisations.

Lesson 4 • Non-Equilibrium Statistical Mechanics

Introduces Boltzmann transport equation, linear response theory, and fluctuation-dissipation theorem. Connects microscopic dynamics to transport coefficients.

Lesson 1 • Canonical Quantisation of Fields

Quantises scalar, spinor, and vector fields using commutation and anti-commutation relations. Fock space and creation/annihilation operators are central tools.

Lesson 2 • Path Integral Formulation

Derives the path integral from the canonical formalism and applies it to scalar and gauge fields. Functional methods and generating functionals are introduced.

Lesson 3 • Renormalisation and Loop Corrections

Treats ultraviolet divergences, dimensional regularisation, and renormalisation schemes. Running coupling constants and the renormalisation group equation are derived.

Lesson 4 • Classical Field Theory

Extends Lagrangian mechanics to fields using the Euler-Lagrange field equations. Noether's theorem connects symmetries to conserved currents.

Lesson 1 • Condensed Matter Field Theory

Applies QFT methods to many-body systems, superconductivity, and the quantum Hall effect. Effective field theories and emergent phenomena are emphasised.

Lesson 2 • Introduction to String Theory

Introduces bosonic and superstring actions, worldsheet quantisation, and the string spectrum. Provides conceptual entry into beyond-Standard-Model physics.

Lesson 3 • Spontaneous Symmetry Breaking and Topology

Analyses Goldstone's theorem, topological defects, and instantons. Connects symmetry breaking to phase transitions and non-perturbative phenomena.

Lesson 4 • Renormalisation Group Methods

Develops Wilsonian renormalisation group, fixed points, and scaling near criticality. Bridges QFT renormalisation and statistical mechanics universality.