I’ve added static images of the atomic orbitals from the app.
http://curvatureofthemind.com/images/atomic/
Archives for May 2011
Mondrian meets javascript
The first poster my wife got for me after we were married was a Mondrian print. I love how he created such pleasing images from such simple forms. Now there is a web app for creating your own Mondrian style creations.
http://www.compositionwithjavascript.com/
What really struck me was how quickly things go off the rails. It only takes a few clicks before a balanced harmonious composition gets too busy or just plain ugly.
Related Images:
Electron sausages?
I just paused writing an article where I tried to give a quick overview of quantum mechanics.
Ha Ha
It ended up being a few paragraphs, a few images, and a crap load of links to Wikipedia. I’m not going to write anything like that anytime soon, and definitely not in a single blog post. I’m going to stick with summaries of the projects I develop and slowly work my way up to wordier subjects. Writing is the hardest part for me, so if you don’t have a bit of background in quantum mechanics, this is going to go over your head a little bit.
Like I’ve said many times in the past, I’ve looked at and derived these equations many times. Writing these apps has helped me understand them better. Here is what I’ve learned from the orbital viewer.
The wavefunctions with m=0 have a phase which is constant in space. This is pretty common in one dimensional bound states like the infinite square well or the harmonic oscillator. Because of that, I didn’t realize how weird that is. These states correspond to electrons that are frozen in space. It’s like the quantum uncertainty of the electron is completely balanced out by the compressive electrostatic force almost like little electron sausages. There is no classical correspondence to these states. There are no stationary planetary orbits.
The states with positive or negative m values are closer to classical circular orbits. The complex exponential factor adds a constant velocity around the axis. For a given energy slower electrons lie closer to the axis and are more spread out along it. As the rotation increases, the electron moves further out and becomes more concentrated on the plane orthogonal to the axis. This creates a series of stacked doughnuts.
As the energy increases for the same angular momentum, inner currents are added with alternating phases. There are a number of different ways to see this. In the full view these are added as nested doughnuts. In the slice view with the intensity cranked up, these show up as inner circles, and the nested doughnuts show up as pie shaped wedges.
This only shows up in rotational mode. The standing mode has nodes around the axis of rotation, which makes the situation visually complicated. Unfortunately many images of these orbitals show the standing waves. Using the complex exponential factor for the rotation instead of the individual elements has been a boon.
I’d never really considered what went into that factor. The complex exponential represents a completely spread out constant velocity motion. I’d thought about it a little as that’s the basic description of a quantum plane wave solution, but I think that’s a post for another day.
Related Images:
Fuzzy and indistinct
One of the things that really strikes me about the orbital renderings that I’ve done is how fuzzy and indistinct the renderings are. One of the main reasons I added the slice view is that I had such a hard time understanding what I was looking at. The outer layers many times completely obscured the inner structures. They aren’t the clear pictures I’ve looked at ever since high school chemistry classes.
Another is how much of a difference having control makes. Twirling the mouse wheel and spinning the image around gives me a much better idea of how these things fit together. What looks like a complete blur at one angle will resolve itself into a set of rings with just the slightest change of angle and intensity.
This really is a foreign realm. Hopefully my demos are helping to make things clearer for people. I’ll be trying my best to describe the triples of numbers indexing each orbital. I’ve learned a lot about them over the past few months I’ve been working with this stuff.
Related Images:
Atomic Orbitals now a chrome experiment
I’ve finally got some code accepted as a chrome experiment. This time it’s a renderer for atomic orbitals using webGL. The technique isn’t so much a ray tracer as much as a ray shader. It sums the probability distribution over rays passing through the orbitals. I’m thinking about ways to adapt it to a solid version next, plus some fun with black holes.