My Math Forum Quantum wave packet propagation, how to use it in FFT?

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 January 29th, 2011, 07:20 AM #1 Newbie   Joined: Oct 2010 Posts: 2 Thanks: 0 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: $\Psi(x, t+dt)= F^{-1}\left{e^{-i\frac{\hbar^2 k^2}{2m} \frac{dt}{\hbar}} F\left{e^{-iV(x)\frac{dt}{\hbar}}\Psi(x,t)\right}\right}$ Which when scaled to dimensionless the time evolution step can be written as: $\Psi(x, t+dt)= F^{-1}\left{e^{-ik^2 dt} F\left{e^{-iV(x)dt}\Psi(x,t)\right}\right}$ 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.... Thanks

 Tags fft, packet, propagation, quantum, wave

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