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NRQM10final

NRQM10final - Physics 216 Final Exam Spring 2010 FINAL EXAM...

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Physics 216 Final Exam Spring 2010 FINAL EXAM INSTRUCTIONS : This is an open book exam. You are permitted to consult the textbooks of Shankar and Baym, your handwritten notes, and any class handouts that are posted to the course website. One mathematical reference book is also permitted. No other consultations or collaborations are permitted during the exam. In order to earn total credit for a problem solution, you must show all work involved in obtaining the solution. However, you are not required to re-derive any formulae that you cite from the textbook or the class handouts. The point value of each problem is indicated in the square brackets below. 1. [30] An electron is placed in a potential V ( vector r ) = e 2 r + β ( r 2 3 z 2 ) , where β is a small parameter. Neglect the spin of the electron. (a) Compute the shifts of the n = 2 energy levels (you may neglect fine-structure effects) using first order perturbation theory. Indicate the relative positions of the energy levels. (b) Suppose that a weak uniform magnetic field B is applied in the z -direction. Determine its effect on the levels obtained in part (a) to first order in B . (c) Repeat part (b) assuming that the weak uniform magnetic field is applied in the x -direction.

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NRQM10final - Physics 216 Final Exam Spring 2010 FINAL EXAM...

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