Electron Diffraction to Tchaikovsky Waltz of the Flowers

Did this about 10 years ago for my physics degree final year project - numerical solutions to the time-dependent Schrödinger Equation (TDSE) applied to electron diffraction. Primarily we were interested in the effects of different slit geometries, as this had never been studied before (for example there's no way you could analytically solve Kirchoff's diffraction theory to anything other than 1-D slits, that is, slits without thickness and funny shapes) - all is performed in dimensionless units.

The electron is modelled here as a wavepacket, that is, a Gaussian distribution superimposed with a sinusoidal wave term, and it interacts in the TDSE with the potential boundary of a double-slit wall, I also investigated other potentials and confines, including an elliptical potential, which was an idea based on what was then a recent publication by IBM laboratories on their STM atom manipulation on substrates - in particular the Stadium Corral. I wanted to approximate the effect they observed with wave effects on the surface state electron density, with the peaks at the foci of the ellipse. They observed that an impurity at one focus led to the disappearance of the peak at the other focus, due to the wave nature to the electron distribution. I never quite got that far as it would have required a lot more computing power (and it was way beyond the objective of the project), but focusing of the electron packet can be observed.

The most advanced desktop PCs I had at my disposal were PII 300 MHz machines - I commandeered 4 machines in our IT room (which got me in trouble with IT dept for never logging out - I disabled their auto logout/reboot scripts which ran a disk cleaner, deleting all user files after midnight - they even blocked my account for a couple of days!) - these machines spent the next month solving the TDSE for a number of conditions via the predictor-corrector method, approximating the differential equations with finite steps, in good old Fortran. This method, however, results in two opposing initial directions for the wave packet to move in, hence the electron splits in two.

Time-dependence therefore suggests that the resulting data be presented in some sort of movie (though not just a movie - time averaged plots can and was also done besides this, for comparison with classical diffraction), so the final probability distribution data was then rendered frame by frame in Matlab. At that time Matlab was a bit basic, you couldn't automatically grab each frame and convert into a movie like you can now. Consequently each frame had to be manually saved as a bmp, all 7000 or so, then imported into some basic animation package, I forget what is is now. For a bit of fun I added the marvellous Waltz of the Flowers by Tchaikovsky. Nobody can write music like he did!

The "finé" at the end was a play on the French word for finished - "fini" - all the French people I knew / met at university seemed to say "é" at the end of everything!

Category:

Science & Technology

Tags:

• electron
• difrraction
• qauntum
• numerial
• computation
• time
• depedent
• Schroedinger
• Equation
• Tchaikovsky
• Waltz
• of
• the
• Flowers

[audecify]

excellent...I came for the song but I stayed for the science.

[blakegriplingph]

Fly away, little moth, FLY!

[SuperVasiliki]

Science avec patience le supplice est sûr.. Arthur Rimbaud

Congratulations! It's excellent!!! Vasiliki

[kazzaflaz]

The beauty of science!

Wonderful!

Thank-you for putting this up, and the hard work that went into it.

Tchaicovsky's 'Walze of the Flowers', from 'The Nutcracker', goes perfectly <3 love it x

[rosescentedshit]

brought a teer to my eye

[Prancer1231]

double slit with convex curvature  lol

[baiyubin]

sha x

[hypercarbon]

is this not from the nut cracker?

[TomStoneMemphis]

And this is why we see interferentions if there is a homogenic light and a small hole in barrier.

[Alguienqueandaporahi]

Guau! Great job.