Why Does My FFT-Based Split Operator Simulation Produce Unexpected Results?

[coelurus]

Hi! This is my first post on these forums.

I'm having some problems with the split operator + FFT algorithm to solve the Schrödinger equation in time. A real Gauss curve in a zero potential environment should simply flatten out, but I get two peaks as the following Matlab run shows:

http://coelurus.thorntwig.se/data/pics/splitop.jpg"
http://coelurus.thorntwig.se/data/tjo.m"

The real problem I assume is that I have no experience at all in using FFT for numerical simulations similar to this method and I can't find any good references on it either.
Any hints, ideas or pointers would be much appreciated!

EDIT: I found a "solution", but I am not sure how to interpret it yet. I had a look in the WavePacket package and it seems that one has to shift both position and momentum space (in Matlab, one would use "fftshift") before and after each FFT. If anybody knows a rigid answer to that I would be overjoyed :) So yes, it works, but I'd like to see why...

 

[Jhero]

Hi there! I'm glad to see you're working on the Schrödinger equation using the split operator + FFT algorithm. It's a powerful technique for solving time-dependent problems in quantum mechanics.

From your post, it seems like you're encountering some unexpected results with your simulations. I can understand your frustration, as it can be difficult to find good references on this method. However, there are a few things you can try to troubleshoot your issue.

First, make sure you are using the correct parameters for your simulation. The split operator + FFT algorithm relies on accurate values for the wavefunction, potential, and time step. Double check your code and input values to make sure they are correct.

Another thing to consider is the size of your simulation grid. If it is too small, you may not be capturing all of the relevant features of the wavefunction. Try increasing the size of your grid and see if that helps with the issue you are experiencing.

You mentioned that you had a look at the WavePacket package and found a solution involving shifting both position and momentum space before and after each FFT. This is a common technique used in FFT-based simulations, and it helps to ensure that the results are accurate and consistent. I would recommend incorporating this into your code and seeing if it improves your results.

Finally, if you're still having trouble, it may be helpful to reach out to other researchers or experts in this field for advice. They may be able to provide some insight or point you towards additional resources that could help.

Good luck with your simulations, and don't get discouraged! It can take some trial and error to get everything working smoothly, but I'm sure you'll get there. Keep us updated on your progress!