A Mathematical Primer on Quantum Mechanics / by Alessandro Teta.

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A Mathematical Primer on Quantum Mechanics / by Alessandro Teta.

9783319778938
3319778935
9783319778921
3319778927

Cham : Springer International Publishing : Imprint : Springer, 2018.

English

1 online resource (xi, 259 pages) : illustrations.

10.1007/978-3-319-77893-8 doi

QC173.96-174.52

530.12

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.

Includes bibliographical references and index.

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UNITEXT for physics.

Print version: 9783319778921

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