Tuesday, October 11, 2016

quantum mechanics - Schrodinger equation for a Hamiltonian with explicit time-dependence?


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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