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Quantum Theory for Mathematicians

Brian C. Hall
Publisher: 
Springer
Publication Date: 
2013
Number of Pages: 
554
Format: 
Hardcover
Series: 
Graduate Texts in Mathematics 267
Price: 
89.95
ISBN: 
9781461471158
Category: 
Textbook
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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 Sef-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.- V Advanced Topics in Classical and Quantum Mechanics.- 20 The Path-Integral Formulation of Quantum Mechanics.- 21 Hamiltonian Mechanics on Manifolds.- 22 Geometric Quantization on Euclidean Space.- 23 Geometric Quantization on Manifolds.- A Review of Basic Material.- References.​- Index.