Two Slit Diffraction Interference by Iterating the Schrodinger Equation

This animation shows the two dimensional (2D) propagation of two gaussian envelope wave packets as governed by the Schrodinger equation. This animation shows how the two diffracting wave packets progress through the near field and result in the expected interference pattern in the far field. The maxima of the interference are controlled by the well known equation
d*sin(theta)=m*lambda
where m is an integer (e.g. (-2, -1, 0, 1, 2))and theta is the angle from the horizontal (white rays). The boundary between the near and far field is marked on the graphic as the intersection of the red rays which are at angles theta except in the opposite sense from the white rays. Note that the final traces of psi*psi (white plots) on the right side of the graphic line up with the white rays as expected. The rule of thumb diffraction solution is valid only in the extreme far field of the slits. Many parameters are variable in this animation and they are pretty well defined by the titles of the sliders.

I have deliberately allowed the learner to adjust the variables beyond the ranges where valid propagation results are obtained. Important parameter for this are the pair (Gridding Half Height and kx) which, if made small enough, will easily run the diffracting wave packet beyond the gridded vertical half widths. Effectively, beyond the gridded width and height, the potential is infinite and results in strong reflections. Just be aware that when you see reflections from the upper and lower bounds of the gridded region that the plot data is no longer valid.

Note that, when plotting real, imagniary, or phase, the wavefronts are perpendicular to the trajectory as they must be. The total desktop computer time for completion of the diffraction is usually about 2 minutes.