Free Online Edition
Quantum Mechanics

This book proposes a rigorous formalization of modern quantum mechanics. Going beyond the scope of conventional introductory textbooks, it develops the essential tools of mathematical physics, from Hilbert spaces to advanced spectral theory, including topology and geometry.
This treatise is intended for readers who seek, beyond computational practice, to understand the logical necessity and foundation of the structures in use. The text addresses interpretational issues directly, with a detailed analysis of the measurement problem and decoherence, while also presenting alternative theories and their experimental constraints.
Intended for master's students, doctoral students, and researchers, it aims at a comprehensive command of the theory, uniting technical rigor with conceptual depth.
About the BookContents
Explore the Themes
General Introduction and Foundational Experiments
Historical experiments that invalidate classical mechanics.
Open theme →Theme 02Hilbert Spaces and Dirac Notation
Hilbert space structure, topological dual, and Dirac notation in finite and infinite dimension.
Open theme →Theme 03Postulates and Applications
Core axioms of the theory, interpretations, and physical consequences of measurement. Computational methods and operator tools to connect postulates with concrete predictions.
Open theme →Theme 04Linear Operator Theory
Topology of Hilbert spaces, bounded and unbounded linear operators, and spectral theory.
Open theme →