Advanced Quantum Physics

(Core graduate Course)

Detailed program

Weeks 1-3: Recap of basic notions

• including ladder operators.
• coherent states.
• Feynman path integrals.

  Weeks 4-7: Quantization of fields

• bosonic creation and annihilation operators.
• the elastic field and phonons.
• the electromagnetic field and photons.
• absorption, radiation, and scattering of photons.

  Weeks 8-11: Second quantization of many-body systems

• fermionic creation and annihilation operators.
• systems of interacting fermions and bosons.
• canonical transformations.
• electron pairing and the BCS theory of superconductivity.

  Weeks 12-13: Relativistic quantum mechanics

• Klein-Gordon equation.
• Dirac equation.