Academic catalogue

Degrees incorporating this pedagocial element :

• Master in Nanosciences and nanotechnologies

Description

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".

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