Number of hours
- Lectures 12.5
- Projects 0
- Tutorials 12.5
- Internship 0
- Laboratory works 0
ECTS
ECTS 3.0
Goal(s)
The objective of this lecture is to provide the basic quantum mechanical tools for advanced theoretical descriptions of condensed matter problems, that is, dealing with a large number of identical particles, obeying quantum statistics. We describe the quantum statistics for fermions and bosons. We introduce the so-called second quantized quantum formalism.
Contact Clemens WINKELMANNContent(s)
In this course, we will study a selection of the topics listed below:
Chapter 1: Quantum statistics and theoretical tools in quantum mechanics
Density matrix operator.
Introduction to Green's functions.
Quantum states of identical particles.
Bosons, Fermions, quantum statistics.
Chapter 2: Bosons and light-matter interactions
Vector potentials and gauge choice.
Classical light-matter Hamiltonian.
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
Cooper pairs, Bogoliubov transformation
Prerequisites
Single-particle quantum mechanics: Dirac formalism, angular momentum, perturbation theory
Test
Semester 8 - The exam is given in english only 
Bibliographic work (1/3) + final exam (2/3)
Travail bibliographique (1/3) + examen final (2/3)
Additional Information
Semester 8 - This course is given in english only
Course list
Curriculum->Engineering degree->Semester 8
Bibliography
G. Baym, Lectures on Quantum Mechanics.
C. Cohen-Tannoudji et al., Mécanique Quantique tome III, "Fermions, bosons, corrélations et intrication"