Advanced quantum physics

This course aims to introduce and develop several fundamental concepts and tools of non-relativistic quantum physics necessary for understanding the physical processes describing the interactions between the elementary constituents of matter and radiation. We will also address 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 Schrödinger's equation for complex physical problems (e.g., variational method, WKB approximation, etc.). Understand the fundamental elements of diffusion processes and know how to apply them in simple situations (e.g., diffusion through an isotropic potential). Know how to use density matrix formalism for the treatment of open quantum systems and its application in quantum optics (optical Bloch equations). Know the fundamentals of quantum mechanics representation based on path integrals and know how to apply them to the calculation of the propagator of a model system (harmonic oscillator).

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

Recommended prerequisites:

- Quantum Physics

- Atoms-Molecules-Radiation

- Analytical Mechanics

Continuous assessment

• 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 and path integral methods