## Quantum Theory: A Mathematical ApproachThis 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

3 | |

9 | |

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 |

425 | |

429 | |