*Prof. Michael Thies (IQG, FAU Erlangen)*

Quantum mechanics has benefitted a lot from exactly solvable and yet physically relevant problems, in particular the harmonic oscillator and the H atom. Whereas the analogue of the harmonic oscillator is easy to identify in quantum field theory (free bosonic fields), it is more difficult to find analytically solvable, interacting models which could play the part of the H atom in quantum field theory. We argue that self-interacting fermionic field theories in 1+1 dimensions in the limit of infinitely many flavors (Gross-Neveu and Nambu-Jona-Lasinio models) of infinitely many flavors (Gross-Neveu and Nambu-Jona-Lasinio models) could fill this gap. In this talk I will focus on the full analytic solution of time dependent scattering problems of composite states in these models, using the relativistic Hartree-Fock approach.