Quantum Theory I, Fall 2002

Abstract:: Topics include uncertainty relation, observables, eigenstates, eigenvalues, probabilities of the results of measurement, Transformation Theory, equations of motion, and constants of motion. Symmetry in Quantum Mechanics, Representations of Symmetry Groups. Variational and Perturbation Approximations. Systems of Identical Particles and Applications. Time-Dependent Perturbation Theory. Scattering Theory - Phase Shifts, Born Approximation. The Quantum Theory of Radiation. Second Quantization and Many-Body Theory. Relativistic Quantum Mechanics of One Electron. 8.321 is the first semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: Hilbert spaces, observables, uncertainty relations, eigenvalue problems and methods for solution thereof, time-evolution in the Schrodinger, Heisenberg, and interaction pictures, connections between classical and quantum mechanics, path integrals, quantum mechanics in EM fields, angular momentum, time-independent perturbation theory, density operators, and quantum measurement.

Quantum Theory II, Spring 2003

Abstract:: A two-semester subject on quantum theory, stressing principles: uncertainty relation, observables, eigenstates, eigenvalues, probabilities of the results of measurement, transformation theory, equations of motion, and constants of motion. Symmetry in quantum mechanics, representations of symmetry groups. Variational and perturbation approximations. Systems of identical particles and applications. Time-dependent perturbation theory. Scattering theory: phase shifts, Born approximation. The quantum theory of radiation. Second quantization and many-body theory. Relativistic quantum mechanics of one electron. This is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation.