PROFESSOR: The molecules and Born-Oppenheimer approximation. OK, we all know that molecules are a lot harder to solve than atoms, and even atoms are not that easy once you have more than one electron because of the electrostatic repulsion, but molecules are significantly different in that one of the greatest simplicities that we had with atoms is that the atom is such that the potential created by the nucleus is spherically symmetric. When you have a molecule you have separate nuclei and therefore your spherical symmetry is gone, and whether you have one electron or more than one electron, there is no spherical symmetry. All our tools of angular momentum don't help us much. We have to start the problem anew. So the difficulty with molecules is basically that the potential for the electrons, where they move is not spherically symmetric. There is another thing that helps us, however, is that there's a nice separation of mass scales. You have the mass, little m, of t...
Welcome back to recitation. In this video, I'd like us to find an antiderivative of the function 1 over x squared minus 8x plus 1. So I'll give you a while to work on it, and then I'll come back, and I'll show you how I started. So welcome back. Well, what we'd like to do is, find an antiderivative to 1 over x squared minus 8x plus 1. And how we're going to do that, is we're going to use the technique completing the square. And I'm going to set up the problem, I'm going to get it to a certain place, and then I'm going to let you finish it. And how do you know if you got the right answer? Well, you actually take a derivative of your answer, and see if it gives you back 1 over x squared minus 8x plus 1. That's how you can check. So let's start off. If I want to complete the square, let's just remind ourselves how to complete the square on this quadratic. So I'd like something right here that makes this a perfect square...
[SQUEAKING] [RUSTLING] [CLICKING] HONG LIU: So in the last lecture, we have concluded the discussion of fermions. And now, we go to the last missing piece before we can talk about the QED. It's how to quantize the Maxwell field, OK? How to get photon, OK? And so today, we start. OK? So this is a short chapter. I think we should be able to finish it just this week in two lectures. So first, let me just remind you of some aspects of the classical Maxwell theory. And then we will talk about this quantization, OK? So the Lagrangian, say, for the classical Maxwell theory can be written as-- Lagrangian density can be written as F mu nu. So F mu nu is just the standard-- partial mu A nu equal to partial nu A mu. And the J mu is just the electromagnetic current. OK. J mu just electromagnetic current. OK. And then so from this Lagrangian density, then you can derive the equation motion, which is just the Maxwell equation, OK? So the Maxwell equation is given by partial mu F mu...
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