Advanced Quantum Mechanics


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 Notes

  • Lecture 2: Hamiltonian of a charged particle in electromagnetic fields.

Lecture Notes

 Video of Lecture


 

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.

Lecture Notes

Video

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

Lecture Notes

Video


 

Week Three

Ahranov and Bohm Effect; Magnetic Monopoles
  • Lecture 5: Ahranov and Bohm Effect

Lecture Notes

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,

Lecture 7

Video

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

Lecture 8

Video

Theoretical and Mathematical Physics @ LUMS