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Can you recommend a good book that discusses several methods for the numerical solution of time-dependent and time-independent Schrödinger equation? I have searched the internet several times but could not find good references.

It would be very helpful if the book also contained matlab/python examples.

I am trying to solve the TDSE in strong laser field, and trying to implement the split operator method or Crank-Nicholson method.

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  • $\begingroup$ you can check this page physics.bu.edu/~py502 for a nice discussion on numerical solution of Schrodinger equation. $\endgroup$ – mas Aug 1 '16 at 18:11
  • $\begingroup$ That said, how strong is your laser field? How many electrons, in how many dimensions, and with what sort of atomic potential? What regime are you interested in, and what physics are you trying to model? All of these will have a strong effect on what methods and software to use. $\endgroup$ – Emilio Pisanty Aug 1 '16 at 19:18
  • $\begingroup$ Actually the field is quite strong $E~10^9 $ V/cm. I am trying to model high order harmonic generation. Initially from single active electron then in several electrons. $\endgroup$ – hsinghal Aug 2 '16 at 1:26
  • $\begingroup$ @EmilioPisanty thanks for pointing out in right direction. I will try to read it fully. If you have some more elaborate literature please give me the same. $\endgroup$ – hsinghal Aug 2 '16 at 2:21
  • $\begingroup$ Note that in strong fields a field strength in V/cm will mostly be met with blank stares - a field strength of 0.36 a.u. or an intensity of $4.8\times 10^{15}\:\mathrm{W/cm^2}$ are much more useful. That's pretty toasty for HHG unless you're doing helium - are you sure you're not saturating the ionization? If you do you won't have any harmonic emission because you won't have any neutrals left to do the emission. $\endgroup$ – Emilio Pisanty Aug 2 '16 at 10:01