2D - Wavepacket step-through integrator

[physgun]

Using the initial Gaussian conditions, calculate the real and imaginary components for integer and half-integer delta T

[physgun]

There's a problem with our integrator: It uses data at t-1, t, and t+1. Which is fine except for the beginning of the integrator, where only t = 0 has the Gaussian starting values and t = 1 has a bunch of zeroes. We can't calculate t = 1 because that would require t = 0 and t = -1, which doesn't exist. It can only start at t = 2, which skips a step entirely.

[orbeckst]

You might have to "back extrapolate" using a simpler integration scheme. If you have, for example, the initial dpsi/dt as one of your initial conditions, then you can use the simple difference scheme to calculate what t-1 should be.

[physgun]

I found the problem: The initial conditions need to be applied to the real array at t = 0 and to the imaginary array at t = 1 (a half step, as 0, 2, 4, etc.. are full steps). Reviewing the textbook, it appears the integrator is intended to start at t = 2. The integrator now works!

[physgun]

Sort of. The system probability, while not blasting off to 1e576 anymore, is still hovering around 2 and 3 after awhile. Obviously, it needs to be close to 1 for about 2 to 3 decimals. Still need to find the last remaining discrepancy.

[ashurmanator]

I have a feeling that if we aren't able to get sensible solutions to this problem using the current integrator by the end of Friday that we should shift gears and attempt to use the simpler 1D iterator and expand it to 2D rather than the 2D specific calculations for R and I.