Many-body quantum mechanics

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Goal: This course gives an introduction to the concepts of many-body quantum mechanics. It describes the quantum statistics of bosons and fermions, and the quantum properties of systems composed of many identical particles. The main theoretical ingredient for this purpose is the creation and annihilation operators of quantum particles, in what is sometimes called the "second quantization formalism". This course is only accessible to students who registered to the Graduate School program Quantum (UE PT2).

Content

  • Chapter 1: Quantum statistics and theoretical tools in quantum mechanics
    Density operator
    Bosons, Fermions, quantum statistics
    Quantum states of identical particles
  • Chapter 2: Bosons and light-matter interactions
    Electromagnetic field quantization, field creation and annihilation operators
    Fock states, coherent states
    Jaynes-Cummings Hamiltonian and vacuum Rabi oscillations
    Bose-Einstein condensation and Gross-Pitaevski equation
  • Chapter 3: Fermionic systems
    Introduction to fermionic creation and annihilation operators
    Fermi sea: electrons and holes
    Hartree-Fock approximation
    Hubbard model
    Cooper pairs, Bogoliubov transformation
Published on June 5, 2021
Updated on September 8, 2023