Lectures on Quantum Mechanics:A Primer for Mathematicians

图书简介

Quantum mechanics is one of the principle pillars of modern physics. It also remains a topic of great interest to mathematicians. Since its discovery it has inspired and been inspired by many topics within modern mathematics, including functional analysis and operator algebras, Lie groups, Lie algebras and their representations, principle bundles, distribution theory, and much more. Written with beginning graduate students in mathematics in mind, this book provides a thorough treatment of (nonrelativistic) quantum mechanics in a style that is leisurely, without the usual theorem-proof grammar of pure mathematics, while remaining mathematically honest. The author takes the time to fully develop the required mathematics and employs a consistent mathematical presentation to clarify the often-confusing notation of physics texts. Along the way the reader encounters several topics requiring more advanced mathematics than found in many discussions of the subject, making for a fascinating course in how mathematics and physics interact.

Preface (in five short acts); Prolegomenon; Part I Nonrelativistic Quantum Mechanics; 1. The Harmonic Oscillator: Classical verses Quantum; 2. The Mathematical Structure of Quantum Mechanics; 3. Observables: Self-adjoint Operators and Expectation Values; 4. The Projection Postulate Examined; 5. Rigged Hilbert Space and the Dirac Calculus; 6. A Review of Classical Mechanics; 7. Hamilton-Jacobi Theory *; 8. Classical Mechanics Regain’d; 9. Wave Mechanics I: The Heisenberg Uncertainty Principle; 10. Wave Mechanics II: The Fourier Transform; 11. Wave Mechanics III: The Quantum Oscillator; 12. Angular Momentum Operators I: Basics; 13. Angular Momentum Operators II: Representations of su(2); 14. Angular Momentum Operators III: The Central Force Problem; 15. Wave Mechanics IV: The Hydrogenic Potential; 16. Wave Mechanics V: Hidden Symmetry; 17. Wave Mechanics VI: Representations and Group Characters; 18. Angular Momentum Operators IV: Addition Rules, etc.; 19. Wave Mechanics VII: Pauli’s Spinor Theory; 20. Cli ord Algebras and Spin Representations *; 21. Many Particle Quantum Systems; 22. The EPR Argument, Nonlocality, and Bell’s Inequalities; 23. Ensembles and Density Operators; 24. Bosons and Fermions; 25. The Fock Space for Indistinguishable Quanta; 26. A Brief Introduction to Quantum Statistical Mechanics; 27. Quantum Dynamics; 28. Unitary Representations, Symmetry, and Conservation Laws; 29. The Feynman Formulation of Quantum Mechanics; 30. A Mathematical Interlude: Gaussian Integrals; 31. Evaluating Path Integrals I; 32. Evaluating Path Integrals II; References; Epilogue; Resources for Individual Exploration; Bibliography; Index.

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Lectures on Quantum Mechanics:A Primer for Mathematicians 量子物理学讲义：数学家指南 物理学史

Lectures on Quantum Mechanics:A Primer for Mathematicians

量子物理学讲义：数学家指南
物理学史