Can I write a Schrodinger equation for time-dependent Hamiltonian like this:
$$i\hbar\frac{d}{dt}\psi(t) = H(t)\psi(t)$$
and then perform Euler integration like this:
$$\psi(t+\Delta t) = (1-\frac{i}{\hbar} H(t)\Delta t)\psi(t)$$
We can do this when $H$ is time-independent for very small $\Delta t$. But when $H$ is time-dependent is it valid to do this?
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