Yes, exp(-iHt) means the vector state is rotating as time passes, and it rotates faster when the Hamiltonian (energy) is bigger. This rotation gives the wave li

Yes, exp(-iHt) means the vector state is rotating as time passes, and it rotates faster when the Hamiltonian (energy) is bigger. This rotation gives the wave like behavior. Slightly related, there is an old video of Feynman where he tries to teach quantum mechanics to some art students, and he explains this complex rotation and its effects without any reference to math.