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.

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Quantum Mechanics
2026

Contents

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Theme 01

General Introduction and Foundational Experiments

Historical experiments that invalidate classical mechanics.

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Theme 02

Hilbert Spaces and Dirac Notation

Hilbert space structure, topological dual, and Dirac notation in finite and infinite dimension.

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Theme 03

Linear Operator Theory

Topology of Hilbert spaces, bounded and unbounded linear operators, and spectral theory.

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Theme 04

Postulates

Core axioms of the theory, interpretations, and physical consequences of measurement.

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