Review of classical and quantum dynamics, Quantization of Classical Systems and Quantum Hamiltonian of a charge moving in electromagnetic fields.
Readings: Shankar chapter 2.
- Lecture 1: Review of Lagrangian and Hamiltonain dynamics; Quantization of classical system.
- Lecture 2: Hamiltonian of a charged particle in electromagnetic fields.
Landau levels and Quantum Hall Effect; Gauge Invariance in Quantum Mechanics;
- Lecture 3: Classical and quantum dynamics of electrons in a constant magnetic field, Cyclotron motion, Landau levels and wave functions.
- Lecture 4: Degeneracy of Landau levels, Flux Quantization, Gauge Invariance of Quantum Dynamics.
Ahranov and Bohm Effect; Magnetic Monopoles
- Lecture 5: Ahranov and Bohm Effect
- Lecture 6: Magnetic Monopoles
Adiabatic Theorem; Berry’s Phases; Identical Particles and Fock Space
- Lecture 7: Adiabatic Theorem, Dynamical and Geometrical Phases, Berry’s Phase for Magnetic Moment, Ahranov Bohm as Berry’s Phase,
- Lecture 8: Identical Particles; Fermions, Bosons and Anynons; Yang-Baxter; Fock Basis for Bosons.