Advanced Quantum Physics

This course is designed to introduce and develop several fundamental concepts and tools of non-relativistic quantum physics necessary for understanding the physical processes that describe the interactions between the elementary constituents of matter and radiation. We 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., the variational method, the 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). Be able to use the density matrix formalism to analyze open quantum systems and its application in quantum optics (optical Bloch equations). Understand the fundamentals of the path integral formulation of quantum mechanics and be able to apply them to calculating the propagator of a model system (harmonic oscillator).

Basic skills in quantum physics (equivalent to the third year of a bachelor’s degree in physics). A solid grasp of the basic mathematical tools (Hilbert spaces, linear algebra, Fourier transforms, Dirac distribution) used in quantum mechanics.

Recommended prerequisites:

- Quantum Physics

- Atoms, Molecules, and Radiation

- Analytical Mechanics

Ongoing Assessment

• Reminders and Fundamental Principles
• Symmetry Theory and Conservation Laws
• Approximation Methods
• Identical Particles and Second-Order Quantification Formalism
• Open Systems and the Density Matrix Formulation
• Introduction to Diffusion Theory
• Functional and Path Integral Methods