The Schrodinger equation is just restating something you may already know if you studied physics. The Hamiltonian is the generator of time translations. Look a

The Schrodinger equation is just restating something you may already know if you studied physics. The Hamiltonian is the generator of time translations. Look at it again with that understanding in your head: https://en.wikipedia.org/w/index.php?title=Special:MathWikibase&qid=Q165498 https://en.wikipedia.org/w/index.php?title=Special:MathWikib... H acting on a state gives you the time translation of the state. That's the crux of it.