Two Potential Slit Diffraction Interference by Iterating the Schrodinger Equation

This animation shows the two dimensional (2D) propagation of a rectangular envelope wave packet as governed by the Schrodinger equation. In this case the grid with two slits is represented by a potential split so that there are two apertures to let some of the original packet through. The initial wave packet is rectangular and it has gaussian rolloff on its boundaries to avoid the diffraction due to sharp edges. The potentials that make up the two slit grid also has gaussian rolloff to avoid the diffraction that sharp edges would cause. The animation shows how the diffracting wave packet progresses through the near field and results in the expected interference pattern in the far field. The angles, theta, of the maxima of the interference are controlled by the well known equation
d*sin(theta)=m*lambda
where m is an integer (e.g. m={-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 (Green trace at the right hand side of the graphic) 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 parameters 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 significant reflections from the upper and lower bounds to the right of the gridded region that the plot data is not as valid.

The total desktop computer time for completion of the diffraction is usually about 5 minutes. After the diffraction is complete a movie that runs much faster can be started.