The figure illustrates an important topic discussed in this course, the principle of least action: From all paths between the points q₁ and q₂ in configuration space, a systems takes the one which renders its action functional stationary.

In this key lecture we follow the traditional approach, coping with wave functions and Schrödinger's equation (and, of course, Heisenberg's famous uncertainty relation), one-dimensional example problems (including the omnipresent harmonic oscillator), angular momentum and centrally symmetric eigenvalue problems (not avoiding the all-important Hydrogen atom), approximation procedures and applications (mostly, but not exclusively, based on time-independent and time-dependent perturbation theory), ...

Well, this is where the advanced stuff actually begins, but also where, unfortunately, the summer term usually comes to an end.

The figure illustrates one of the most important phenomena encountered in elementary quantum mechanics: The tunneling of a wave packet through a barrier in a double-well potential.

In the lecturer's humble opinion, this is the most rewarding of the basic physics courses, because one derives almost anything from almost nothing. At the end of this lecture, we (hopefully) understand semiclassical statistical mechanics as well as quantum mechanical statistical physics, formulated in the microcanonical, canonical, and grand canonical ensembles. Special emphasis is given on the study of Bose and Fermi gases, together with some of their most prominent appearances in physics.

One of the most important topics covered in this course concerns the differences between the classical Maxwell-Boltzmann (MB) and the quantum mechanical Bose-Einstein (BE) and Fermi-Dirac (FD) statistics. The figure shows average grand canonical occupation numbers pertaining to these statistics as functions of the scaled energy.

The figure illustrates the celebrated Bloch-Zener scenario: The wave packet of a quantum particle in a periodic lattice potential subjected to a static external force is depicted as a contour plot vs. position (horizontal) and time (vertical). The wave packet performs Bloch oscillations, here with a fairly small amplitude because the force is quite strong. Once per period, it undergoes a Zener transition to a higher band, then escaping to infinity on a parabolic trajectory corresponding to a free particle accelerated by the force.

This course is targeted towards the explanation of superconductivity given by Bardeen, Cooper, and Shrieffer. Their theory, arguably, constitutes one of the most beautiful achievements of theoretical physics, capturing the delicate interplay between several basic mechanisms and effects, reducing them to the bare essentials, and making rock-hard predictions. After recapitulating some key experimental findings, we study electron-phonon interaction, and verify the existice of Cooper pairs. We then turn to the mean-field approximation, utilize the Bogoliubov transformation, and formulate the BCS self-consistency equation. Having constructed approximate solutions of the gap equation we explore the thermodynamics of BCS superconductors, and (if time permits) investigate the current-carrying state.

The figure depicts an elementary process underlying superconductivity: An first electron (symbolized by the straight lines right) emitts a phonon (wavy line), which then is absorbed by a second electron. One of the key topics covered in this course is the finding that this phonon exchange gives rise to an attractive force between the negatively charged electrons, leading to the formation of the famous Cooper pairs.