We know there are some (many actually) exactly solvable models, like the Hydrogen atom, the harmonic oscillator, etc. But these models are solvable often only in the sense that the eigenstates or eigenvalues are solvable. In other words, the corresponding time-independent Schroedinger equation is exactly sovable.

How about the time-dependent Schroedinger equation? How many models are exactly solvable in the sense of its dynamics?


closed as too broad by Kyle Kanos, Yashas, Jon Custer, ZeroTheHero, Cosmas Zachos May 3 '17 at 13:10

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.