A Mathematical Primer on Quantum Mechanics

Beschreibung

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.

Explains theory through detailed mathematical analysis of simple but relevant solvable models

Proposes numerous exercises to stimulate interactive learning

Offers the necessary background for those embarking on advanced courses on mathematical methods in quantum mechanics

Autor*in

Alessandro Teta

Themen in »A Mathematical Primer on Quantum Mechanics«

Quantum mechanics textbook for mathematicians Mathematical physics textbook Dynamics of a quantum particle Solvable models in quantum mechanics Operators in Hilbert spaces elementary theory of Hilbert spaces scattering theory for mathematicians

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“The presentation is well-structured and easy to follow, with ample examples and exercises. It can hence be used both as a basis for a course on this topic as well as for self study. It is a welcome addition to the textbook literature on this subject.” (G. Teschl, Monatshefte für Mathematik, Vol. 191 (3), 2020)
“This book fills the gap between the elementary classical and quantum mechanics … and higher-level mathematics required to study more advanced books. Indeed, after reading this Primer a student would have enough motivation and basic understanding of the theory of (un)bounded linear operators to read … .I highly recommend it especially for physics students, who after reading this Primer should be fully prepared and motivated to study a more advanced references … .” (Arsen Melikyan, zbMATH 1394.81006, 2018)
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