Quantum Theory: A Mathematical Approach

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Springer, Dec 1, 2014 - Science - 445 pages
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This book was inspired by the general observation that the great theories of modern physics are based on simple and transparent underlying mathematical structures – a fact not usually emphasized in standard physics textbooks – which makes it easy for mathematicians to understand their basic features.

It is a textbook on quantum theory intended for advanced undergraduate or graduate students: mathematics students interested in modern physics, and physics students who are interested in the mathematical background of physics and are dissatisfied with the level of rigor in standard physics courses. More generally, it offers a valuable resource for all mathematicians interested in modern physics, and all physicists looking for a higher degree of mathematical precision with regard to the basic concepts in their field.

 

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Contents

1 Introduction
3
2 Classical Mechanics
9
General Principles
21
4 Quantum Mechanics of a Single Particle I
53
5 Quantum Mechanics of a Single Particle II
65
6 The Harmonic Oscillator
73
7 The Hydrogen Atom
89
Atomic Structure
105
17 Concluding Remarks
265
Part II Supplementary Material
277
18 Topology
279
19 Measure and Integral
289
20 Manifolds
299
Hilbert Space
313
22 Probability Theory
353
23 Tensor Products
361

9 Many Particle Systems
115
10 Review of Classical Statistical Physics
139
11 Quantum Statistical Physics
157
12 Physical Theories as Algebraic Systems
171
13 Quantization
187
14 Scattering Theory
217
15 Towards Relativistic Quantum Theory
235
An Introduction
247
24 Lie Groups and Lie Algebras
371
25 Generalized Functions
393
26 Diracs BraKet Formalism
401
27 Algebras States Representations
405
List of Authors Cited
419
Index of Persons
425
Subject Index
429
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About the author (2014)

Peter Bongaarts taught for many years theoretical and mathematical physics at the University of Leiden, the Netherlands

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