Advanced quantum physics

The aim of this course is to introduce and develop several fundamental concepts and tools of non-relativistic quantum physics needed to understand the physical processes describing the interactions between the elementary constituents of matter and radiation. It will also cover second quantization and the path integral formulation of quantum mechanics, which provide the ideal framework for the development of quantum field theory and its various applications (e.g. high-energy physics, condensed matter physics).

Master the various techniques for solving the Schrödinger equation for complex physical problems (e.g. variational method, WKB approximation, etc.). Know the fundamentals of diffusion processes and know how to apply them in simple situations (e.g. diffusion by an isotropic potential). Know how to use the density matrix formalism for open quantum systems and its application to quantum optics (optical Bloch equations). Know the fundamentals of the path integral representation of quantum mechanics and apply it 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 (Hilbert 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 diffusion theory
• Functional methods and path integrals