## Mathematical Foundations of Quantum Mechanics |

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### Contents

Introductory Considerations | 3 |

2 The Original Formulation of Quantum Mechanics | 6 |

The Transformation Theory | 17 |

Hilbert Space | 28 |

Abstract Hilbert Space | 34 |

2 The Geometry of Hilbert Space | 46 |

3 Digression on the COnditions A E | 59 |

4 Closed Linear Manifolds | 73 |

2 The Statistical Interpretation | 206 |

3 Simultaneous Measurability and Measurability in General | 211 |

4 Uncertainty Relations | 230 |

5 Projections as Propositions | 247 |

6 Radiation Theory | 254 |

Deductive Development of the Theory | 295 |

2 Proof of the Statistical Formulas | 313 |

3 Conclusions From Experiments | 328 |

5 Operators in Hilbert Space | 87 |

6 The Eigenvalue Problem | 102 |

7 Continuation | 107 |

8 Initial Considerations Concerning the Eigenvalue Problem | 119 |

9 Digression of the Existence and Uniqueness of the Solutions of the Eigenvalue Problem | 145 |

10 Commutative Operators | 170 |

11 The Trace | 178 |

The Quantum Statistics | 196 |

General Considerations | 347 |

2 Thermodynamical Considerations | 358 |

3 Reversibility and Equilibrium Problems | 379 |

4 The Macroscopic Measurement | 398 |

The Measuring Process | 417 |

2 Composite Systems | 422 |

3 Discussion of the Measuring Process | 437 |