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In this case study, we're going to see how we can create a photo illustration of your work. The idea here is to show how a liquid battery works for a final illustration. So first, create photographic bits and pieces and put them all together. Think of it just as if you were drawing the pieces and putting those sketches together. After I met with the researchers for a brainstorming meeting, I got all this material from them, including a diagram that described my idea to create a model of how a liquid battery works. This is the way I imagined the shoot to go. OK first, I would take an optical quality cuvette and would then pour the mercury and the water into the cuvette and somehow suspending with a clamp, a strip of metal foam, which is an important part of the science. And because I was imagining a full container of this material after making the image, I would then crop out the right side-- we don't need to see the clamping device-- and then flip the left side, o...

PROFESSOR: So case A-- weak Zeeman effect. So what are our states here? We discovered that and we know those are the coupled basis states. And the states of H0 tilde eigenstates-- they are approximate eigenstates-- are the states n, l, j, mj. And the energies were energies dependent on n and j. So the 1S 1/2, 2S 1/2, 2P 1/2, and 2P 3/2. Roughly, to remind you of what happened, the original states were shifted, and we used the j quantum number in here. And those are our multiplets. Those are our multiplets. And we have a lot of degeneracy as usual. So this is degeneracy here and degeneracy here because a multiplet P 3/2 is j equal 3/2. And that's four states. Here you have two states, and here you have two states as well. So quite a bit of states that are degenerate. So in principle, when we do the Zeeman splitting, we may have to consider the full matrix n, l, j, mj, delta H Zeeman, nl prime j m prime j. So what are our degeneracies? Our degeneracies are when you have...

PROFESSOR: Let's do a case that this mostly solvable and illustrates all these things. It's a very entertaining case. It's called Landau-Zener transitions. For these two people, Lev Landau, who you've probably heard from Landau and Lifshitz. He's the first person that tried to do this. And Zener did it more carefully. In fact, apparently found that Landau made a factor of two error. And the paper of Zener, it's actually quite nice, and it's a very nice example that illustrates the physics of this transition. So we'll devote the rest of the lecture to that Landau-Zener thing. OK. So it will give us a little bit into the spirit of the adiabatic approximation in the language that Berry used. So Landau-Zener transitions. OK, Zener and Landau were interested in molecules, and some way of thinking of molecules is to think of nuclei as fixed, separated by some distance R, and then you assume they are fixed, and they're separated by some distan...