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Unformatted text preview: stationary state energies and their degeneracies. The columns of the table should be as shown below: l n k nl 2 Ma 2 E nl / ~ 2 degeneracy 2. Griﬃths Problem 4.9. Note that you should be able to relate this problem to Question 1 of Homework 5, and hence to quote a pair of equations whose simultaneous solution determine the groundstate energy. 3. Griﬃths Problem 4.14. 4. Griﬃths Problem 4.15. 5. The hydrogen atom. (a) Show that h x i = h y i = h z i = 0 in any stationary state ψ nlm of the hydrogen atom. Hint: Write x , y , and z in spherical coordinates and focus on the angular integrals. You may ﬁnd helpful the relation Y m l ( πθ, φ ) = (1) l + m Y m l ( θ, φ ). (b) Calculate h r i , h r 2 i , h x 2 i , and h z 2 i in the ψ 210 state of hydrogen. Hint: Integrals over θ are often simpliﬁed by the identity Z π f (cos θ ) sin θ dθ = Z 11 f ( μ ) dμ for any function f ( μ ). 6. Griﬃths Problem 4.45....
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This note was uploaded on 12/15/2011 for the course PHY 4604 taught by Professor Field during the Fall '07 term at University of Florida.
 Fall '07
 Field
 mechanics, Work

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