>>10195484

Try adding a few more oscillators to your graph: y = A1sin(B1x+C1) + A2sin(B2x+C2) + ... Then try fiddling with the parameters. Try to get the graph to form a large "bump" at x = pi/2. (Hint: you probably won't want to touch any of the C parameters right now).

"Did you do it, little Jimmy? Wow that sure is good; great job, little Jimmy... Now, in your graph, where is the electron?" Well, if we look at it, it appeara that the electron is _mostly_ at the bump, but there are other bumps, too, and really its not the sharpest bump possible. In fact it turns out that in order to have a perfect bump, representing an electron at only one point in space, you need infinitely many sine waves at different frequencies added together.

Now its time to dive a little deeper into the physics. In this case when we look at the sine waves making up an electron, we say that an x-value represents a position, and a sine wave's frequency represents a momentum. So a perfectly peaked wave would mean that the electron is at one point in space, but that its momentum simultaneously takes every possible value. On the other hand, a single sine wave represents an electron with one perfectly-defined momentum, but that is everywhere simultaneously.

"Sure, sure", you say, "but what exactly is 'momentum'? Why do we care?"

Well, momentum is related to the speed, or velocity, of the electron. When the momentum is higher, the electron is moving faster, it has a higher velocity.

So our little electron is in a bit of a conundrum. It can be in one place but move around completely unpredictably, move at a perfectly certain speed but be everywhere at once, or somewhere in between, having a sort-of well-defined momentum and a sort-of well-defined position. It can't be in one spot and moving at one speed simultaneously.

In essence, these two values are in a constant tug-of-war. Finally, we can get a basic understanding of why the electrons in an atom don't collapse towards the protons.