Quantum Theory for Mathematicians

Includes Reference (545-548) and Index

1.The Experimental Origins of Quantum Mechanics
2. A First Approach to Classical Mechanics
3. A First Approach to Quantum Mechanics
4. The Free Schrödinger Equation
5. A Particle in a Square Well
6. Perspectives on the Spectral Theorem
7.The Spectral Theorem for Bounded Self-Adjoint Operators: Statements
8. The Spectral Theorem for Bounded Self-Adjoint Operators: Proofs
9. Unbounded Self-Adjoint Operators
10. The Spectral Theorem for Unbounded Self-Adjoint Operators
11. The Harmonic Oscillator
12. The Uncertainty Principle
13. Quantization Schemes for Euclidean Space
14. The Stone–von Neumann Theorem
15. The WKB Approximation
16. Lie Groups, Lie Algebras, and Representations
17. Angular Momentum and Spin
18. Radial Potentials and the Hydrogen Atom
19. Systems and Subsystems, Multiple Particles

Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone–von Neumann Theorem; the Wentzel–Kramers–Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics.The numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basics of L2 spaces and Hilbert spaces. The final chapters introduce readers who are familiar with the theory of manifolds to more advanced topics, including geometric quantization.