Lectures on quantum mechanics for material scientists

Abstract

When speaking of quantum mechanics, one has typically a physics or chemistry student in mind. However, research on materials is now so advanced that students of material science must be trained to understand and above all use those deepest concepts of quantum mechanics that were reserved to physics students in the past. It is along these lines that these lectures discuss the fundamental concepts of modern Quantum Physics such as the failure of classical mechanics, the postulates and mathematical structure of Quantum Physics, the electronic structure of atoms, molecules and solids, the electron spin and time dependent perturbations. The lectures are constructed in such a way that the various concepts are introduced by starting from the explicit and detailed treatment of a simple example. These particular cases are then generalized and put into a ''moderately '' rigorous framework -- the word ''moderately'' meaning that the mathematics is not worked out in details but the essential steps are rigorous enough to withstand practical applications. The present manuscript summarizes the content of the various lectures. The lectures were distributed over a semester at ETH Zurich (about 13 weeks, four hours per week). The course included a set of problems that were intended to complement the lectures themselves with concrete examples and that were solved weekly by the students (one hour per week). Some of the experiments presented contain a link to the site ''Vorlesungsexperimente Departement Physik'' of ETH Zurich. The team that prepared these experimental demonstrations over the years has supported the present lectures with a large amount of experiments that could be performed in-situ and in real time. They also made their work available online. I am grateful to the team for their work in supporting these lectures, in particular, and the entire physics lecture businnes at ETH Zurich. The knowledge used to prepare these lectures was acquired by reading a large amount of literature on the subject. In particular, I would like to quote the lectures on quantum mechanics held by the late Prof. R. Jost at ETH Zurich during the academic year 1977-1978 and the manuscript by the late Prof. Hunziker. The present lectures show my personal understanding of the subject. This understanding also emerged during the interaction with the many students that frequented my courses. A thank goes also to them.