midterm 1 solutions

midterm 1 solutions - Physics 519 MIDTERM Name Spring 2013...

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Physics 519 MIDTERM Name: Spring 2013 5/1/13 80 pts — “1 point per minute” Exam procedures. Please write your name above. Please sit away from other students. If you have a question about the exam, please ask. This is a closed book exam. All relevant formulae are given on the exam. If you think a needed equation is not provided, please ask. Note that questions extend to the back of the sheets. Write your answers on the exam. I have tried to leave ample space, but if you need more, use additional paper and be sure to write “519 Midterm” and your name on the top of each page. Unless stated otherwise, it is necessary for full credit that you explain the logic of your calculation, deriving any results that you use. Standard results given in the equations sheet do not, however, require explanation. 1
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1. Hydrogen perturbation theory. (60 pts) The 1 s and the 2 p z wave functions of the hydrogen atom are: ψ 1 s ( r ) = e - r/a 0 πa 3 0 , ψ 2 p z ( r ) = r cos θ e - r/ 2 a 0 32 πa 5 0 , where a 0 is the Bohr radius, r = | r | is the radial coordinate, and θ is the polar angle coordinate defined with respect to the z -axis. You might find the following integral helpful:
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  • Spring '13
  • Lin
  • Physics, mechanics, Electric charge, Fundamental physics concepts, Perturbation theory, Effective charge

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