Timeline for Why do we assume the potential is independent of time in the Schrödinger equation?
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| May 12, 2019 at 19:38 | comment | added | FunctionalDefect | No, of course I am not doubting it can be solved numerically; just don't understand how the standard methods apply, which to me amounts to RK (I have very limited numerical PDE experience). Thanks for the resources. | |
| May 12, 2019 at 19:23 | comment | added | Emilio Pisanty | Regarding numerical methods: are you seriously doubting that the TDSE can be solved numerically? If you've only been shown a restricted class of Runge-Kutta solvers, then go look for a text that deals with broader variants of the method. This google search is a good starting point - the zoo of methods for time-dependent QM is far too broad to mention here. Pretty much every method here, other than eigenvalue methods, can be used for time-dependent problems. | |
| May 12, 2019 at 19:17 | comment | added | Emilio Pisanty | Good examples from my neck of the woods are high-order harmonic generation and above-threshold ionization in the tunnelling regime. Doubtless there are others. | |
| May 12, 2019 at 19:10 | comment | added | FunctionalDefect | Right, of course I had forgotten about studying time-dependent perturbations. Could you name some examples where the probe would be out of the perturbative regime (or just a system that might be studied without perturbation theory)? As for numerical methods, I do not see how to use e.g. Runge-Kutta, since my understanding is that RK4 solves equations of the form $\partial_t \Psi = f(x,\Psi)$ but now we have $f(x,t,\Psi)$ since $V$ depends on $t$ in addition to $x$. | |
| May 12, 2019 at 18:29 | vote | accept | FunctionalDefect | ||
| May 12, 2019 at 6:16 | history | edited | Emilio Pisanty | CC BY-SA 4.0 |
added 369 characters in body
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| May 12, 2019 at 6:09 | history | answered | Emilio Pisanty | CC BY-SA 4.0 |