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A Course in Mathematical Physics 3 : Quantum Mechanics of Atoms and Molecules

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概要 In this third volume of A Course in Mathematical Physics I have attempted not simply to introduce axioms and derive quantum mechanics from them, but also to progress to relevant applications. Reading ...the axiomatic litera ture often gives one the impression that it largely consists of making refined axioms, thereby freeing physics from any trace of down-to-earth residue and cutting it off from simpler ways of thinking. The goal pursued here, however, is to come up with concrete results that can be compared with experimental facts. Everything else should be regarded only as a side issue, and has been chosen for pragmatic reasons. It is precisely with this in mind that I feel it appropriate to draw upon the most modern mathematical methods. Only by their means can the logical fabric of quantum theory be woven with a smooth structure; in their absence, rough spots would . inevitably appear, especially in the theory of unbounded operators, where the details are too intricate to be comprehended easily. Great care has been taken to build up this mathematical weaponry as completely as possible, as it is also the basic arsenal of the next volume. This means that many proofs have been tucked away in the exercises. My greatest concern was to replace the ordinary cal culations of uncertain accuracy with better ones having error bounds, in order to raise the crude manners of theoretical physics to the more cultivated level of experimental physics.続きを見る
目次 1 Introduction
1.1 The Structure of Quantum Theory
1.2 The Orders of Magnitude of Atomic Systems
2 The Mathematical Formulation of Quantum Mechanics
2.1 Linear Spaces
2.2 Algebras
2.3 Representations on Hilbert Space
2.4 One-Parameter Groups
2.5 Unbounded Operators and Quadratic Forms
3 Quantum Dynamics
3.1 The Weyl System
3.2 Angular Momentum
3.3 Time-Evolution
3.4 The Limit t ? ± ?
3.5 Perturbation Theory
3.6 Stationary Scattering Theory
4 Atomic Systems
4.1 The Hydrogen Atom
4.2 The Hydrogen Atom in an External Field
4.3 Helium-like Atoms
4.4 Scattering Theory of Simple Atoms
4.5 Complex Atoms
4.6 Nuclear Motion and Simple Molecules.
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登録日 2020.06.27
更新日 2020.06.28