Quantum Paths: Fourth Lesson

In this fourth and final lesson we demonstrate the different distributions that can be obtained from various patterns of slits on the wall. There is only one new concept here, that the phase and probability of the slits is relevant. Basically, in the double slit expirement we assumed that the electron arrives at each slit with the same phase and that the electron had a 50% probability of going through either slit. In fact, through various physical apparatuses we can change the probability of the electron going through the various slits and we can also change the phase the electon has as it reaches each respective slit. The simulation below allows you to explore a multiple slit expirement where you may vary the location and number of the slits and you may also vary the probability and phase associated with the electron as it arrives at each slit.

We make a major simplifying assumption in the calculation below that we had not made before. Rather than sum over an explicit set of 100 paths we use the value that comes out mathematically when one does the full sum over all possible paths. Hence, we do not draw an intermediate line for paths as in previous expirement, but we obtain more accurate results and significantly reduce the computation time.

Instructions
Click anywhere in the bottom half of the display in the upperleft corner to create a slit. Clicking in the upper half selects the endpoint on the screen to graph. Click the "Left" or "Right" buttons to have the point on the screen move in the corresponding direction, and press "Stop" to stop the movement. Clicking within the circles at the bottom change the phase and probability associated with the slit of the corresponding color. Clicking the remove button below a circle removes that slit.