David Tong: Quantum Mechanics

David Tong: Lectures on Quantum Mechanics

This is an introductory course on quantum mechanics. The lecture notes are around 120 pages. Please do email me if you find any typos or mistakes.


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Content


  • 1. Introduction:   PDF
    The wavefunction, normalisation, superposition. The Schrödinger equation, the Hamiltonian, conservation of probability, collapse of the wavefunction. The double slit experiment.
  • 2. A Quantum Particle in One Dimension:   PDF
    The free particle; a particle on a circle; the infinite potential well; the gaussian wavepacket. The harmonic oscillator energy spectrum and wavefunctions as Hermite polynomials. Bound states, general results, the double well potential, scattering and tunnelling.
  • 3. The Formalism of Quantum Mechanics:   PDF
    States, the inner product. Operators and observables, eigenfunctions and eigenvalues, Hermitian operators. Measurement, expectation values. Commutation relations and the Heisenberg uncertainty principle. Interpretations of quantum mechanics: hidden variables, copenhagen, many worlds, shut up and calculate.
  • 4. A Quantum Particle in Three Dimensions:   PDF
    Angular momentum: commutation relations, spherical harmonics and Legendre polynomials. The 3d harmonic oscillator and 3d bound states. The hydrogen atom energy spectrum and the wavefunctions. A pre-quantum quantum history: spectroscopy, the Bohr model and the photon. A first look at renormalisation: a delta-function potential in two dimensions.


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