anderkve
commented
1 year ago Hi @nigarabbasova!
Is it still okay for us to present our results with this box setup, or would you rather have us regenerate our results with just the wall and the slits?
Nice plot of the potential! It's perfectly fine to use that for your results. Just make sure to include the plot of the potential. Given that we don't run the simulations for very long, I suspect the difference in the results will be minimal (probably not even noticeable.)
Currently, we only see the central maxima in our normalised probability figure, without maxima of other orders (1st, 2nd, etc).
That sounds correct :)
This is not exactly what one would expect to see with an actual single-slit experiment, since both the central maxima and smaller order maxima are supposed to be present. So in our results, could this be because of the placement of our detector, i.e it is placed far away from where the diffraction happens, and we only catch the central maxima? Or is this because of the Gaussian wave packet that we are using? Usually, monochromatic light sources are used in actual experiments and personally, my intuitive physical understanding of Gaussian wave-packets is quite limited, so analysing the single-slit diffraction with them is a bit confusing :)
There are quite a few things here that are different from the typical analytical, monochromatic and static case seen in textbooks:
-
The finite timespan of high amplitude at any y point along the vertical line at x=0.8 (or any other place), introduced by the fact that the wavepacket starts out confined in the x direction (which of course also introduces elements of more than one frequency). So the interference pattern at x=0.8 will depend on what timestep we choose to plot it.
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The non-zero depth of the slit. Our slit is a little bit like a short tunnel (you can try adjusting it!)
To more easily get an intuition for the behavior of the wavepacket compared to the usual monochromatic textbook scenario, I stronglyt recommend you make an animation where you just look at the behavior of the real (or imaginary) part of the wavefunction. Then it's also easy to see the dominant wavelength, which may give you some clue as to what you should expect if this was a monochromatic case.
PS: If you do this, I'd recommend you read the wavelength of a plot rather than derive it analytically. Due to some sub-optimal choices I made when scaling away the constants in the Schr. eq, there may be some missing factors of 2 that might confuse you if you do it analytically.
nigarabbasova
Hi Anders!
We have modelled the potential as an actual box, i.e we did not just put a wall in the middle with the slits, but have also added the top, bottom and sides of the box, and set them equal to some high constant. It doesn't look like you explicitly asked us to do that in the project description. Is it still okay for us to present our results with this box setup, or would you rather have us regenerate our results with just the wall and the slits? To make life easier, I am attaching a figure of our box potential. Vsingle.pdf :)
Another question that we have is about the single-slit diffraction pattern. Currently, we only see the central maxima in our normalised probability figure, without maxima of other orders (1st, 2nd, etc). This is not exactly what one would expect to see with an actual single-slit experiment, since both the central maxima and smaller order maxima are supposed to be present. So in our results, could this be because of the placement of our detector, i.e it is placed far away from where the diffraction happens, and we only catch the central maxima? Or is this because of the Gaussian wave packet that we are using? Usually, monochromatic light sources are used in actual experiments and personally, my intuitive physical understanding of Gaussian wave-packets is quite limited, so analysing the single-slit diffraction with them is a bit confusing :)
Thank you very much for your help!