The aim of the course is the introduction to the basic concepts and theoretical methods used in the problems of modern quantum mechanics and condensed matter physics.
The course is divided in two parts. In the first part, we will thoroughly study the theoretical methods of solving single-particle problems in quantum mechanics: tight-binding approximation for finding the spectrum of periodic systems such as crystals, different methods in time-dependent perturbation theory to study optical properties of quantum systems. Moreover, students will get acquainted with the concept of topology in quantum mechanics.
The second part is dedicated to the basic methods of studying many-body interactions in quantum mechanics. Using the basic problems as examples, we will discuss the simplest yet effective methods of the mean field approximation, diagrammatic technique and path integrals.