The Schrodinger equation for time-dependent Hamiltonian is
$$i\hbar\frac{d}{dt}\psi(t) = H(t)\psi(t) \, .$$
Assuming I knew $\psi(t)$, I want to know $\psi(t+\Delta t)$.
Should I take exponential or use ode solver?
I know that the mathematical solution after one timestep should be (or not?)
$$\psi(t+\Delta t) = e^{-\frac{i}{\hbar}H(t)\Delta t}\psi(t) \, .$$
It gives a different result from using ode solver unfortunately. Which is the most correct one?
expm
function in matlab is what I used. I think it should be pretty accurate in that it keeps a lot of terms. $\endgroup$ – diff Oct 17 '16 at 22:03