Quantum Mechanics
This is an introductory course on quantum mechanics. The lecture notes are around 130 pages. Please do email me if you find any typos or mistakes.
If you enjoy the notes, a greatly expanded version is available as a textbook.
These lecture notes are also available in HTML format, which may be more accessible for screen readers.
Introduction
The wavefunction, normalisation, superposition. The Schrödinger equation, the Hamiltonian, conservation of probability, collapse of the wavefunction. The double slit experiment.
A Quantum Particle in One Dimension
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.
The Formalism of Quantum Mechanics
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.
A Quantum Particle in Three Dimensions
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.