Lectures

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Lecture 1: Second quantization formalism for harmonic oscillator

  • Example: Coherent states
  • Example: Phonons in solids

Lecture 2: Second quantization formalism for bosons

  • Example: Magnons in magnetic materials.
  • Example: Bogoliubov theory of superfluids.

Lecture 3: Second quantization formalism for fermions

  • Example: Hubbard clusters.
  • Example: Hartree-Fock theory of electrons in metals.
  • Example: BCS theory of superconductivity.

Lecture 4: Time-dependent perturbation theory

  • Example: Dyson vs. Magnus expansion for driven harmonic oscillator.

Additional references

S. Blanes, F. Casas, J. A. Oteo and J. Ros, A pedagogical approach to the Magnus expansion, Eur. J. Phys. 31, 907 (2010). [PDF]

Lecture 5: Floquet theory of periodically driven quantum systems

Lecture 6: Berry phase and wavefunctions for time-dependent quantum systems

Lecture 7: Quantization of electromagnetic field

Lecture 8:

Lecture 9:

Lecture 10:

Lecture 11:

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