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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.

hsinghal
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  • you can check this page http://physics.bu.edu/~py502/ for a nice discussion on numerical solution of Schrodinger equation. –  Aug 01 '16 at 18:11
  • 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. – Emilio Pisanty Aug 01 '16 at 19:18
  • 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. – hsinghal Aug 02 '16 at 01:26
  • @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. – hsinghal Aug 02 '16 at 02:21
  • 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. – Emilio Pisanty Aug 02 '16 at 10:01
  • Note also that doing multiple electrons in the HHG range is not a trivial project, and if you want more than one electron in the continuum it's sort of a PhD-thesis-size project. Do you need to go to full 3D, or are you happy to stay in 1D? Again, all of this will strongly inform the solution space you're interested in. If you're looking for running code then I'd go for Patchkovski and Muller's SCID; if you're looking for entry-level literature then maybe Scrinzi's chapter here is a good start. – Emilio Pisanty Aug 02 '16 at 10:12
  • @EmilioPisanty Thanks I have already checked your question. It is really good but if I can get some book on the subject it will be more in depth information. If you know any such book (for numerical solution of schrodinger equation in general) please let me know thanks in advance. – hsinghal Aug 02 '16 at 16:37

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