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January 29th, 2011, 07:20 AM   #1
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Quantum wave packet propagation, how to use it in FFT?

So I used the split step method on the Schrodinger equation and have produced the following equation:


Which when scaled to dimensionless the time evolution step can be written as:



F above represents the Fourier transform operator acting on the equations.
Now my problem is that I don't know how to implement the above in Fast Fourier Transform.
For example: If I were to take the exponential factor with V(x), do I multiply -iV(x) by dt?
Not sure I understand what is going on here....

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