Lectures on Quantum Mechanics
A Primer for Mathematicians
 Author: Philip L. Bowers, Florida State University
 Publication planned for: July 2020
 availability: Not yet published  available from July 2020
 format: Hardback
 isbn: 9781108429764
Hardback
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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 theoremproof 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 oftenconfusing 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.
Read more A mathematically honest treatment of quantum mechanics suitable for graduate students
 Develops the required mathematics in full while retaining a leisurely style
 Features several topics of interest requiring more advanced mathematics than found in many quantum mechanics texts
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×Product details
 Publication planned for: July 2020
 format: Hardback
 isbn: 9781108429764
 dimensions: 228 x 152 mm
 availability: Not yet published  available from July 2020
Table of Contents
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: Selfadjoint Operators and Expectation Values
4. The Projection Postulate Examined
5. Rigged Hilbert Space and the Dirac Calculus
6. A Review of Classical Mechanics
7. HamiltonJacobi 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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