Introduction to Quantum Mechanics

This module starts from zero prior knowledge and shows the experimental puzzles that classical physics could not explain: black-body radiation, the photoelectric effect and atomic spectra. By the end, the learner can describe each puzzle, state the quantum idea that resolved it, and calculate basic photon and Bohr-model quantities.

1. Black-body radiation and the ultraviolet catastrophe 1 practice exercise
2. The photoelectric effect and the photon 1 practice exercise
3. Atomic spectra and the Bohr model

Building on the photon and Bohr-model results from Module 1, this module shows that matter also has wave properties. It introduces the de Broglie wavelength, the probabilistic meaning of the wavefunction and the uncertainty principle. By the end, the learner can compute matter wavelengths, normalize a wavefunction and estimate minimum uncertainties.

1. de Broglie waves and electron diffraction 1 practice exercise
2. The wavefunction as a probability amplitude 1 practice exercise
3. The Heisenberg uncertainty principle 1 practice exercise

Module 2 described quantum states in words and single functions. This module supplies the mathematics that makes them precise: complex numbers, Fourier analysis, linear operators, eigenvalue problems and Dirac notation. By the end, the learner can apply these tools to compute eigenvalues, expectation values and orthogonality conditions.

1. Complex numbers and Fourier representation of waves 1 practice exercise
2. Operators, eigenvalues and eigenfunctions 1 practice exercise
3. Hermitian operators and orthogonal states 1 practice exercise
4. Dirac notation for states and inner products 1 practice exercise

With the mathematical tools from Module 3, this module derives the central equation of non-relativistic quantum mechanics. It separates stationary states from time evolution and sets out the boundary conditions that any physical wavefunction must meet. By the end, the learner can write and solve the time-independent equation for simple potentials and apply continuity conditions.

1. Deriving the time-independent Schrödinger equation 1 practice exercise
2. The time-dependent equation and stationary states 1 practice exercise
3. Boundary conditions and continuity requirements 1 practice exercise

Using the Schrödinger equation from Module 4, this module solves the standard one-dimensional problems that form the core of most B.Sc. examinations: the infinite and finite well, the tunnelling barrier and the harmonic oscillator. By the end, the learner can solve each system, compute energy levels and transmission probabilities, and interpret the results physically.

1. The particle in an infinite square well 1 practice exercise
2. The finite potential well and bound states 1 practice exercise
3. Quantum tunnelling through a potential barrier 1 practice exercise
4. The quantum harmonic oscillator 1 practice exercise
5. Ladder operators for the harmonic oscillator 1 practice exercise

Module 5 treated one-dimensional systems. This module moves to three dimensions, where the hydrogen atom returns the Bohr energy levels with quantum numbers and orbital shapes. It then develops angular momentum and spin, which the Stern-Gerlach experiment reveals. By the end, the learner can solve the hydrogen radial and angular parts, identify quantum numbers, and use angular momentum commutation relations.

1. Separation of variables in spherical coordinates 1 practice exercise
2. Energy levels and radial wavefunctions of hydrogen 1 practice exercise
3. Quantum numbers and orbital shapes 1 practice exercise
4. Angular momentum operators and their commutation relations 1 practice exercise
5. Electron spin and the Stern-Gerlach experiment 1 practice exercise

Most real systems cannot be solved exactly, so Module 6 gave exact solutions only for idealized cases. This module introduces perturbation theory and the variational method, then uses them with the Pauli principle to describe helium and the filling of atomic shells. By the end, the learner can estimate energy corrections, bound ground-state energies and predict electron configurations.

1. First-order time-independent perturbation theory 1 practice exercise
2. The variational method for ground-state energies 1 practice exercise
3. Identical particles, bosons and fermions 1 practice exercise
4. Helium and electron configurations of atoms 1 practice exercise

Building on the operators and states of Modules 3 to 7, this module addresses what happens when a quantum system is measured and how it evolves in time. It covers the measurement postulate, compatible observables, Ehrenfest's theorem and the first ideas of entanglement. By the end, the learner can predict measurement outcomes and probabilities, check compatibility, and describe an entangled state.

1. The measurement postulate and wavefunction collapse 1 practice exercise
2. Commutators and compatible observables 1 practice exercise
3. Time evolution and Ehrenfest's theorem 1 practice exercise
4. Entangled states and the Bell inequality 1 practice exercise

Using the bound states, tunnelling and spin results of earlier modules, this module connects quantum mechanics to devices and technologies. It covers band theory and semiconductors, lasers, tunnelling-based instruments and the qubit. By the end, the learner can explain how each device depends on a specific quantum result and perform a basic calculation for each.

1. Energy bands and semiconductors
2. Lasers and stimulated emission 1 practice exercise
3. Tunnelling devices and the scanning tunnelling microscope 1 practice exercise
4. Qubits and quantum computing basics 1 practice exercise

Having mastered the core theory and its applications in Modules 1 to 8, the learner now applies it on their own. This module guides a computational project, prepares the learner for careers and interviews, and points to key works, open questions and routes to advanced study. By the end, the learner can complete and present an original quantum project and plan further study or research.

1. Building a numerical Schrödinger solver 1 practice exercise
2. Designing and presenting an original quantum project 1 practice exercise
3. Careers and interview preparation in quantum physics 1 practice exercise
4. Key works, open questions and routes to advanced study 1 practice exercise