**Week One**

###### 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.

### Week Two

###### 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.

Video

- Lecture 4: Degeneracy of Landau levels, Flux Quantization, Gauge Invariance of Quantum Dynamics.

Video

### Week Three

##### Ahranov and Bohm Effect; Magnetic Monopoles

- Lecture 5: Ahranov and Bohm Effect

Video

- Lecture 6: Magnetic Monopoles

Lecture Notes

Videos

##### Home Work 1

### Week Four

##### 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,

Video

- Lecture 8: Identical Particles; Fermions, Bosons and Anynons; Yang-Baxter; Fock Basis for Bosons.

Video