Physics 195bProblem set number 19Due 2 PM, Thursday, March 13, 2003Notes about course:• Homework should be turned in to the TA’s mail slot on the first floorof East Bridge.• Collaboration policy: OK to work together in small groups, and to helpwith each other’s understanding. Best to first give problems a good tryby yourself. Don’t just copy someone else’s work – whatever you turnin should be what you think you understand.• There is a web page for this course, which should be referred to for themost up-to-date information. The URL:http://www.hep.caltech.edu/˜fcp/ph195/• TA: Anura Abeyesinghe, [email protected]• If you think a problem is completely trivial (and hence a waste of yourtime), you don’t have to do it. Just write “trivial” where your solutionwould go, and you will get credit for it. Of course, this means you arevolunteering to help the rest of the class understand it, if they don’tfind it so simple. . .READING: Read the “Second Quantization” course note.PROBLEMS:88. Probability current of a charged particle in an electromagnetic field:Do Exercise 2 of the Electromagnetic Interactions course note.89. The electric field in quantum mec hanics: Do Exercise 3 of the Electro-magnetic In teractions course note.90. Tw o-level fermion system, second quantized: Do Exercise 1 of the Sec-ond Quantization course note.5491. We have been discussing superconductivity as an application of quan-tum mechanics. We considered a very simple model at first, in orderto demonstrate the plausibility of the formation of Cooper pairs. Thescanned notes are available as a link from the Ph 195 home page. Thefirst seven pages are of present interest.(a) Try to make an estimate for how large the Cooper pair is, perhapsby evaluating r orr2 .(b) Turn your estimate into a number, e.g., comparing the size withthe lattice spacing of the superconductor. You will no doubt needto make plausible estimates (guesses?) of unknown
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