By exactly solvable model, people generally mean models whose eigenstates or eigenenergies can be solved analytically. Simple examples are the harmonic oscillator, the infinitely deep square well potential, the hydrogen atom, the Bethe ansatz solvable models (like the 1d Heisenberg model), etc.
However, for many such models, e.g., the Bethe ansatz solvable models, the solvability cannot be generalized to the time domain.
So, is there any example whose dynamics can also be solved exactly? I know the harmonic oscillator is one. Is there any extra nontrivial model?
ps: The Landau-Zener problem is also one, of course.
