Read online: quantumlectures.org
A free, rigorous yet accessible course on quantum mechanics, bridging classical physical intuition with the mathematical formalism of Hilbert spaces, linear operators, and measurement theory. Written for advanced undergraduates and graduate students, and freely readable in the browser (French and English), with KaTeX-rendered mathematics and downloadable per-theme PDFs.
Each lesson is paired with a library of worked exercises — statements, hints, and full solutions — also available as a single downloadable PDF per theme.
Part I — Isolated systems
- Foundational experiments — the historical experiments (Stern–Gerlach, spin) that break classical mechanics and motivate quantization.
- Hilbert spaces and linear operators — the mathematical backbone: inner product spaces, duality, bras and kets, bounded and unbounded operators, spectral theory.
- Postulates — measurement, dynamics, and the interpretation of quantum states built on that formalism.
- Applications — potential barriers, the harmonic oscillator, spin, and quantum dynamics, connecting the postulates to concrete, solvable problems.
The course is under active development. Two further themes are planned to extend the material from isolated, idealized systems toward open, realistic ones:
- Interacting systems — composite states, entanglement, and the dynamics of quantum systems that are no longer isolated.
- Decoherence and quantum measurement — how classical behavior emerges from quantum dynamics, the role of the environment, and the measurement problem.
Further themes and a growing exercise library are expected to follow as the book continues to expand.
Learn Thermo (source) — a companion course on thermodynamics, by Jean-Philippe Bruneton (Université Paris Cité, France).