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Mackey G.W. The mathematical foundations of quantum mechanics: A lecture-note volume

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Mackey G.W. The mathematical foundations of quantum mechanics: A lecture-note volume
W.A. Benjamin Inc., 1963. - 137 pp.
When lecturing on advanced topics the author frequently writes out a more or less complete (and somewhat improved) draft of the lectures actually given and makes them available to the students. This was done in particular for a course in the mathematical foundations of quantum mechanics given at Harvard in the spring of 1960. These notes were corrected, typed, and mimeographed by Messrs. E. Bolker, V. Manjarrez, A. Ramsay, and
M. Spivak and put on sale by the Harvard Mathematics Department. The text of this book is substantially that of those notes. However, several pages have been radically revised, numerous small errors have been corrected, and a short appendix has been added.
The aim of the course was to explain quantum mechanics and certain parts of classical physics from a point of view more congenial to pure mathematicians than that commonly encountered in physics texts. Accordingly, the emphasis is on generality and careful formulation rather than on the technique of solving problems. On the other hand, no attempt is made at complete rigor. In places a complete treatment would have taken us too far afield and in others non-trivial mathematical problems remain to be solved. There are also places where completeness simply seemed more troublesome than illuminating. In sum, we have tried to present an outline of a completely rigorous treatment which can be filled in by any competent mathematician modulo the solution of certain more or less well-defined mathematical problems.
Contents:
Editor's Foreword.
Preface.
Classical Mechanics
Preliminaries.
The Laws of Particle Mechanics.
Generalized Coordinates and Differentiable Manifolds.
Oscillations, Waves, and Hilbert Space.
Statistical Mechanics.
Quantum Mechanics
The Old Quantum Theory.
The Quantum-Mechanical Substitute for Phase Space.
Quantum Dynamics and the Schrodinger Equation.
The Canonical "Quantization" of a Classical System.
Some Elementary Examples and the Original Discoveries of Schrodinger and Heisenberg.
Generalized Coordinates.
Linear Systems and the Quantization of the Electromagnetic Field.
Quantum-Statistical Mechanics.
Group Theory and the Quantum Mechanics of the Atom
Preliminaries.
Basic Notions in the Theory of Group Representations.
Perturbations and the Group Theoretical Classification of Eigenvalues.
Spherical Symmetry and Spin.
The n-Electron Atom and the Pauli Exclusion Principle.
Appendix.
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