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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.
List of contents
Preface.- 1. Brief Review of Hamiltonian Mechanics and Electromagnetism.- 2. From Planck's Hypothesis to Bohr's Atom.- 3. Schrodinger Equation.- 4. Linear Operators in Hilbert Spaces.- 5. Rules of Quantum Mechanics.- 6. Free Particle.- 7. Harmonic Oscillator.- 8. Point Interaction.- 9. Hydrogen Atom.- 10. The Cloud Chamber Problem.- References.- Index.
Summary
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.
Additional text
“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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"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)
