Quantum Physics Course

Lesson 1 • Bohr Model of the Atom

Presents Bohr's quantised orbital model and its success in explaining hydrogen spectral lines. Highlights the model's limitations that motivate full quantum mechanics.

Lesson 2 • Einstein and the Photon Concept

Covers Einstein's extension of quantisation to light and the photoelectric effect explanation. Establishes photons as fundamental quanta of electromagnetic energy.

Lesson 3 • De Broglie Matter Waves

Introduces the hypothesis that matter exhibits wave properties characterised by a de Broglie wavelength. Bridges particle and wave descriptions ahead of wave mechanics.

Lesson 4 • Limits of Classical Mechanics

Examines Newtonian mechanics and electromagnetism to identify where classical predictions fail. Sets the stage for understanding why a new physical framework was required.

Lesson 1 • Commutators and Uncertainty Relations

Defines commutator algebra and derives the generalised uncertainty principle from operator non-commutativity. Links mathematical structure to fundamental physical constraints.

Lesson 2 • Linear Algebra Essentials

Reviews vector spaces, inner products, and linear operators as the algebraic backbone of quantum theory. Provides the mathematical vocabulary used throughout the course.

Lesson 3 • Hilbert Space and State Vectors

Defines Hilbert space as the arena of quantum states and introduces state vectors as complete descriptions of quantum systems. Connects abstract maths to physical observables.

Lesson 4 • Hermitian Operators and Observables

Establishes Hermitian operators as the mathematical representatives of physical observables. Proves that Hermitian operators yield real eigenvalues and orthogonal eigenstates.

Lesson 1 • Finite Well and Tunnelling

Extends the square well to finite potential barriers and introduces quantum tunnelling. Demonstrates exponential decay in classically forbidden regions and transmission coefficients.

Lesson 2 • Time-Independent Schrödinger Equation

Applies separation of variables to obtain stationary states and energy eigenvalue equations. Provides the foundation for solving bound-state problems throughout the course.

Lesson 3 • Particle in a Box

Solves the infinite square well as the simplest bound-state problem with exact analytic solutions. Illustrates energy quantisation, zero-point energy, and orthonormal eigenfunctions.

Lesson 4 • Wave Function Interpretation

Defines the wave function and establishes Born's probabilistic interpretation of its modulus squared. Connects the mathematical object to measurable probability densities.

Lesson 1 • Analytic Solution via Hermite Polynomials

Solves the Schrödinger equation for the harmonic oscillator using power series, yielding Hermite polynomial eigenfunctions. Establishes equally spaced energy levels.

Lesson 2 • Coherent States and Classical Limit

Defines coherent states as eigenstates of the annihilation operator and shows they minimise uncertainty. Demonstrates how quantum oscillator behaviour approaches classical motion.

Lesson 3 • Classical Harmonic Oscillator Review

Revisits classical oscillator dynamics and energy to motivate the quantum analog. Establishes the potential energy form used in the quantum treatment.

Lesson 4 • Ladder Operator Algebraic Method

Introduces creation and annihilation operators to derive the energy spectrum algebraically. Demonstrates the elegance of operator methods over direct differential equation solving.

Lesson 1 • Magnetic Moments and Precession

Connects angular momentum to magnetic dipole moments and derives Larmor precession in external fields. Provides the quantum basis for magnetic resonance phenomena.

Lesson 2 • Addition of Angular Momenta

Presents Clebsch-Gordan coefficients and rules for combining two angular momenta into total angular momentum states. Essential for multi-particle and spin-orbit systems.

Lesson 3 • Orbital Angular Momentum Operators

Defines orbital angular momentum operators from position and momentum and derives their commutation relations. Establishes the algebraic structure governing all angular momentum.

Lesson 4 • Spin Angular Momentum

Introduces intrinsic spin as a purely quantum mechanical degree of freedom with no classical analogue. Derives spin-1/2 matrices and two-component spinors.

Lesson 1 • Hydrogen Atom Wave Functions

Constructs complete hydrogen wave functions by combining radial and spherical harmonic parts. Visualises orbital shapes and probability densities for key states.

Lesson 2 • Radial Wave Functions

Solves the radial Schrödinger equation for hydrogen, yielding associated Laguerre polynomial solutions. Derives the principal quantum number and Bohr radius from first principles.

Lesson 3 • Fine Structure and Corrections

Introduces relativistic and spin-orbit corrections that split hydrogen energy levels beyond the Bohr formula. Previews perturbation theory as the tool for computing these shifts.

Lesson 4 • Central Force Reduction

Reduces the two-body Coulomb problem to an effective one-body radial equation using reduced mass. Separates angular and radial degrees of freedom for systematic solution.

Lesson 1 • WKB Approximation

Derives the WKB semiclassical approximation for slowly varying potentials and applies it to tunnelling and quantisation. Connects quantum solutions to classical trajectories.

Lesson 2 • Degenerate Perturbation Theory

Extends perturbation theory to degenerate energy levels by diagonalising the perturbation within the degenerate subspace. Applied to Stark and Zeeman effects.

Lesson 3 • Variational Principle

States the variational theorem and uses trial wave functions to obtain upper bounds on ground-state energies. Demonstrates the method on helium and simple model systems.

Lesson 4 • Time-Dependent Perturbation Theory

Derives transition probabilities for systems driven by time-dependent perturbations using Fermi's golden rule. Applies to absorption, emission, and scattering processes.

Lesson 1 • Quantum Statistical Distributions

Derives Fermi-Dirac and Bose-Einstein distributions from symmetry constraints and compares them to Maxwell-Boltzmann statistics. Connects particle type to macroscopic thermodynamic behaviour.

Lesson 2 • Physical Consequences of Quantum Statistics

Explores Bose-Einstein condensation, Fermi energy in metals, and superfluidity as macroscopic quantum phenomena. Demonstrates how microscopic symmetry drives observable bulk properties.

Lesson 3 • Multi-Electron Atoms

Applies the independent-particle approximation and Hartree-Fock method to multi-electron atoms. Explains periodic table structure through electron configuration and shell filling.

Lesson 4 • Indistinguishability and Exchange Symmetry

Establishes that identical quantum particles are fundamentally indistinguishable and that wave functions must be symmetric or antisymmetric under exchange. Introduces the exchange operator.