Physics 195aProblem set number 7Due 2 PM, Thursday, November 21, 2002Notes 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 sections 1-5 of the “Solving the Schr¨odinger Equation:Resolvents” course note.PROBLEMS:35. Harmonic oscillator in three dimensions: Exercise 2 of the HarmonicOscillator course note.36. Resolvent mathematics: Exercise 1 of the Resolvent course note.37. More resolvent mathematics: Exercise 2 of the Resolvent course note.38. Still more resolvent mathematics: Exercise 3 of the Resolvent coursenote.2339. Green’s function solution of the infinite square well: Exercise 4 of theResolvent course note.40. The one-electron atom (review?): We have had a couple of examplesof looking at the qualitative features of wave functions. Now apply thesame reasoning to the one-electron atom. Thus, sketch the effectivepotential and the lowest three radial wave functions (do both R(r)andu(r)=rR(r)) for the 1-electron atom for  = 0. Now do the same forthe qualitative solutions for  = 1. Pay attention to the turning points,and to the dependence at r = 0. Since you have already computed theactual wave functions, you may produce graphs of the functions youobtained. If you do this, however, you should look carefully at yourgraphs and make sure you understand at a physically intuitive level thequalitative