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PROFESSOR: We're finished with WKB. In recitation, you saw some transmission across the barrier and that's also included in the notes. That's an important application of WKB and should look at it. And today we're going to start with a new topic. It's time-dependent perturbation theory. And time-dependent perturbation theory is going to keep us busy for a number of lectures. There's a lot of applications of these ideas and the methods are rather general. Here is the place where we will learn about Fermi's Golden Rule. The kind of rule that is useful for radiation problems, ionization problems, transitions. It's all very applied. Nevertheless, we have to develop the theory carefully and see what are the main concepts. So time-dependent perturbation theory is our subject. Time-dependent perturbation theory. Again, we will begin with a Hamiltonian that is time independent. And we know about it. We call this Hamiltonian H zero. The same name we ...

Okay, so solving successfully finished, and we've got the results. If you had any trouble solving this problem, then you should go into Options in the Solver and select that you want to edit the length of solution time and increase it past 100 seconds. The LibreOffice Solver is not incredibly powerful, so it may need more time to find the solution. We do recommend that if you have access to Excel, that you use Excel instead for integer optimization problems, because Excel is a little bit better with integer optimization. However, you probably got the solution just fine. So you'll want to go ahead and click Keep Result. So now, we can take a look at our solution. So we've got the objective of 4.46. This is not particularly interpretable, until you remember that what our objective is, is the total of all departments percent of target allocation hours reached. So the best possible number that we could get here would be 5, if every department had 100% of their tar...