In this lecture we will start to put atoms together to build simple molecules. We will first use the Born-Oppenheimer approximation, to eliminate slow processes from the study of the fast electron dynamics. Then, we will study simple mechanisms of binding atoms.

We have seen that we can understand matter with increasing complexity from the simple two-level system up to molecules. We further studied, how they can be control by classical electromagnetic fields to a very high accuracy. In the last lecture we also studied how we can understand the electromagnetic field as an ensemble of quantum mechanical photon modes. So in today’s lecture we will focus on the interaction between atoms and light, which is in a particularly clean set-up, namely cavity quantum electrodynamics. The fundamental ingredients are sketched in Fig. [305911].

We are looking into the quantization of the electromagnetic field. How to find the conjugate momenta and how we can identify the photon as a quantized particle.

We will study some basic properties of the laser.

In this lecture we will use the hydrogen atom to study static perturbations in form of external magnetic fields and relativistic effects, leading to the fine structure splitting.

We will continue with some properties of the hydrogen atom. First compare it to the harmonic oscillator, then look into dipole transitions and end with the coupling to static magnetic fields.

In the lecture, we will see how a time dependent coupling allows us to engineer a new Hamiltonian. Most importantly, we will discuss the resonant coupling of two levels and the decay of a single level to a continuum.

In this second lecture we will finish the discussion of the basic cooking recipes and discuss a few of the consequences like the uncertainty relation, the existance of wave packages and the Ehrenfest theorem.

We will discuss today how quantum effects emerge in degenerate gases and how they are connected to problems that come traditionally from condensed-matter physics.

We will finish our discussion by the some words on quantum simulation and quantum computation.

In todays lecture we will study spontaneous emission its connection with absorption and how we can control it certain situations.

After our discussion of extremely simple atoms like hydrogen and helium, we will now discuss the most important properties of more complex atoms. We will see, how we can categorize them and discuss some of the general properties