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Callan C.G. Topics In Advanced Quantum Mechanics

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Callan C.G. Topics In Advanced Quantum Mechanics
Princeton University, 1996. — 189 p. OCR
This course will be a one-semester review of non-relativistic quantum mechanics designed for physics graduate students. It should be useful in helping to prepare for the preliminary exams, but that is not the primary goal of the course. My aim is to make you aware of important modern developments that are not usually covered in didactic/pedagogic courses. We will cover the main topic areas at high speed and I will assume that you already have a pretty good working knowledge of the subject, so undergraduates beware! Ample problem-solving opportunities will be provided and I strongly urge you to do the problems faithfully. There will be
one problem set per week and it will be graded and returned with solutions.
We will denote roughly a week of lecture and problem time to a selection from the following topic list:
1 - One Dimensional Trivia - Exercises with 5 - function potentials to illustrate a number of physics points in a soluble context. Scattering theory, band structure, localization, etc.
2 - Harmonic Oscillator - Coherent states, squeezed states (super accurate measurement applications), Bogoliubov transform
3 - Angular Momentum - standard lore (representation theory, addition theorems, etc.), Wigner-Eckart theorem, selected applications (decay correlations, g-factors, rotators)
4 - Particles in Magnetic Fields - General setup, Landau levels, Bohm Aharonov, Hall effect, Hofstadter problem.
5 - Dirac Equation - An instructive alternative to doing the dull old central potential problem. Extract Pauli theory in large mass limit.
6 - Time Independent Perturbation Theory - the standard story for non-degenerate and degenerate cases, exploration of convergence, demonstration of Borel resummation trick for anharmonic oscillator.
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