# 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.

# Quantum Mechanics on the Web

**Lecture Notes on Quantum Mechanics**by Jeff Greensite**The Feynman Lectures on Physics**Volume III**Quantum Mechanics**by Konstantin Likharev