Alessandro Teta – författare

This book offers a rigorous yet elementary approach to quantum mechanics that will meet the needs of Master’s-level Mathematics students and is equally suitable for Physics students who are interested in gaining a deeper understanding of the mathematical structure of the theory. Throughout the coverage, which is limited to single-particle quantum mechanics, the focus is on formulating theory and developing applications in a mathematically precise manner. Following a review of selected key concepts in classical physics and the historical background, the basic elements of the theory of operators in Hilbert spaces are presented and used to formulate the rules of quantum mechanics. The discussion then turns to free particles, harmonic oscillators, delta potential, and hydrogen atoms, providing rigorous proofs of the corresponding dynamical properties. Starting from an analysis of these applications, readers are subsequently introduced to more advanced topics such as the classical limit, scattering theory, and spectral analysis of Schrödinger operators. The main content is complemented by numerous exercises that stimulate interactive learning and help readers check their progress.

This book offers a rigorous yet elementary approach to quantum mechanics that will meet the needs of Master’s-level Mathematics students and is equally suitable for Physics students who are interested in gaining a deeper understanding of the mathematical structure of the theory. Throughout the coverage, which is limited to single-particle quantum mechanics, the focus is on formulating theory and developing applications in a mathematically precise manner. Following a review of selected key concepts in classical physics and the historical background, the basic elements of the theory of operators in Hilbert spaces are presented and used to formulate the rules of quantum mechanics. The discussion then turns to free particles, harmonic oscillators, delta potential, and hydrogen atoms, providing rigorous proofs of the corresponding dynamical properties. Starting from an analysis of these applications, readers are subsequently introduced to more advanced topics such as the classical limit, scattering theory, and spectral analysis of Schrödinger operators. The main content is complemented by numerous exercises that stimulate interactive learning and help readers check their progress.

In the original formulation of quantum mechanics the existence of a precise border between a microscopic world, governed by quantum mechanics, and a macroscopic world, described by classical mechanics was assumed. Modern theoretical and experimental physics has moved that border several times, carefully investigating its definition and making available to observation larger and larger quantum systems. The present book examines a paradigmatic case of the transition from quantum to classical behavior: A quantum particle is revealed in a tracking chamber as a trajectory obeying the laws of classical mechanics. The authors provide here a purely quantum-mechanical description of this behavior, thus helping to illuminate the nature of the border between the quantum and the classical.

In the original formulation of quantum mechanics the existence of a precise border between a microscopic world, governed by quantum mechanics, and a macroscopic world, described by classical mechanics was assumed. Modern theoretical and experimental physics has moved that border several times, carefully investigating its definition and making available to observation larger and larger quantum systems. The present book examines a paradigmatic case of the transition from quantum to classical behavior: A quantum particle is revealed in a tracking chamber as a trajectory obeying the laws of classical mechanics. The authors provide here a purely quantum-mechanical description of this behavior, thus helping to illuminate the nature of the border between the quantum and the classical.