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Mathematical Foundations of Quantum Mechanics
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Mackey, George Whttps://catalog.mountainview.gov/GroupedWork/1fa2f2c6-d781-7adb-fc3c-dda9168919e6-eng01 Jan 2013 00:00:00 GMT<img alt='Cover Image' src='https://catalog.mountainview.gov/bookcover.php?id=1fa2f2c6-d781-7adb-fc3c-dda9168919e6-eng&size=medium&type=grouped_work&category=eBook'/> Designed for students familiar with abstract mathematical concepts but possessing little knowledge of physics, this text focuses on generality and careful formulation rather than problem-solving. Its author, a member of the distinguished National Academy of Science, based this graduate-level text on the course he taught at Harvard University. Opening chapters on classical mechanics examine the laws of particle mechanics; generalized coordinates and differentiable manifolds; oscillations, waves, and Hilbert space; and statistical mechanics. A survey of quantum mechanics covers the old quantum theory; the quantum-mechanical substitute for phase space; quantum dynamics and the SchrÃ¶dinger equation; the canonical "quantization" of a classical system; some elementary examples and original discoveries by SchrÃ¶dinger and Heisenberg; generalized coordinates; linear systems and the quantization of the electromagnetic field; and quantum-statistical mechanics. The final section on group theory and quantum mechanics of the atom explores basic notions in the theory of group representations; perturbations and the group theoretical classification of eigenvalues; spherical symmetry and spin; and the n-electron atom and the Pauli exclusion principle.