Abstract: In this course, we will introduce the basic notions of quantum theory such as the Hilbert space, observables and time evolution. We will start with examples where the Hilbert space is finite-dimensional such as particle spins and spin chains. We will continue with more complicated examples which involve the Sturm-Liouville operator and the Schrödinger equation.
If time permits, we would like to introduce the following interesting topics: Bethe Ansatz for quantum spin chains, Bell inequalities, semiclassical picture and the WKB approximation, continuous spectrum and scattering theory.
Pre-requisites: linear algebra, differential calculus, some knowledge of classical mechanics is desirable but the facts which are needed will be covered in the course.