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PROFESSOR: Square well. So what is this problem? This is the problem of having a particle that can actually just move on a segment, like it can move on this eraser, just from the left to the right. It cannot escape here. So the way we represent it is the interval 0 to a on the x-axis. And there's going to be two walls, one wall to the left and one wall to the right, and no potential in between. That is, I write the potential V of x as 0, for x in between a and 0, and infinity for x less than or equal to 0, and x greater than or equal to a. So basically the particle can move from 0 to a, and nowhere else. The potential is infinity. Now, this problem, meaning that the wave function-- the particle cannot be outside the interval, means that the wave function must vanish outside the interval. And you could say, how do you know? Well, if the potential is close to infinite amount of energy to be there, so the particle cannot really be there if it's really infinite energy...

BARTON ZWIEBACH: Finite square well. So this brings us also to a little common aside. So far, we could find every solution. Now we're going to write the equations for the finite square well, and we're not going to be able to find the solution. But we're going to understand the solution. So you're going to enjoy a little-- mathematicians usually say it's the most important thing, understanding the solution. Finding it, it's no big deal. But we're physicists as well. So we sometimes have to find the solutions. Even if we don't understand them very well, it's nice to find them. And then you're going to use numerical methods, and this is the part of the course where you're going to be using numerical methods a lot. Here is the finite square well, and now we draw it symmetrically. Here it is. Here is x. We're drawing the potential V of x. It extends from a to minus a. It's 0. This is the 0 of the potential. It's here. And...