Quantum Mechanics with David Tong

The complete Cambridge lecture course — wave functions to the hydrogen atom

Syllabus

  1. Core Lectures

    1. Introduction to Quantum Mechanics: Wave Functions & Probability
    2. Normalisation, Superposition & the Gaussian Wave Function
    3. The Schrödinger Equation
    4. Probability Current, Wave Function Collapse & the Double-Slit Experiment
    5. The Time-Independent Schrödinger Equation & the Free Particle
    6. Wave Packets & the Gaussian Wave Packet
    7. The Harmonic Oscillator: Power Series Solution
    8. Lesson 7
    9. Bound States & the Finite Square Well
    10. Quantum Scattering & Tunnelling
    11. Lesson 9
    12. Quantum Formalism: States as Vectors & Hilbert Space
    13. Observables as Operators: Position, Momentum & Angular Momentum
    14. Eigenvalues, Eigenstates & Measurement Outcomes
    15. Hermitian Operators, Orthonormality & the Eigenbasis
    16. Time Evolution & Quantum Revivals
    17. Measurement, the Born Rule & Expectation Values
    18. Qubits, Pauli Matrices & Electron Spin
    19. Commuting Operators & Shared Eigenstates
    20. Lesson 17
    21. Angular Momentum in 3D: Operators & Commutation Relations
    22. Spherical Harmonics & the Angular Schrödinger Equation
    23. Central Potentials & the Radial Schrödinger Equation
    24. The Hydrogen Atom: Bohr Model to Quantum Numbers
    25. Solving the Hydrogen Atom: Recurrence Relations & Energy Spectrum
    26. Lesson 22