Advanced quantum physics

This course aims at introducing and developing several fundamental concepts and tools of non-relativistic quantum physics necessary to understand the physical processes describing the interactions between the elementary constituents of matter and radiation. The second quantization and the path integral formulation of quantum mechanics will also be discussed as they represent the ideal framework for the development of quantum field theory and its various applications (e.g. high energy physics, condensed matter physics).

To master the different techniques for solving the Schrödinger equation for complex physical problems (e.g. variational method, WKB approximation,...). To know the fundamental elements of the diffusion processes and to know how to apply them in simple situations (ex: diffusion by an isotropic potential). To know how to use the density matrix formalism for the treatment of open quantum systems and its application in quantum optics (optical Bloch equations). To know the foundations of the representation of quantum mechanics based on path integrals and to know how to apply them to the calculation of the propagator of a model system (harmonic oscillator).

Basic skills in quantum physics (L3 level of a physics degree). Good command of basic mathematical tools (Hilbertian spaces, linear algebra, Fourier transform, Dirac distribution) for quantum mechanics.

Recommended Prerequisites:

- Quantum Physics

- Atoms-Molecules-Rayonnement

- Analytical Mechanics

Continuous control

• Reminders and fundamental principles
• Symmetry theory and conservation rules
• Approximation methods
• Identical particles and second quantization formalism
• Open systems and density matrix formalism
• Introduction to the theory of diffusion
• Functional methods and path integrals