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Test4solution

# Test4solution - Name I.D Test#4(Closed Book and Notes...

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Name: Test #4 (Closed Book and Notes, Calculators Allowed) Physics 113B Quantum Mechanics Tuesday, November 29,2011 (Check to see that there arc gpages, including this cover page.) I.D.: Problem 1: Problem 2: Problem 3: Problem 4: Total: lrs lr0 /18 /07 ls0

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l. (15 points)Consider an atom with a single unpaired electron in an externalmagnetic field, B"*t. (a) (3 points) When Be*t (( 861, we say that in the weak field limit. What is the origin of the 861? B,^+ = *duno,!. f,.1J e+ "rlb;h*1 pralur\ thof lL c-ftech4rh- "ef(f-r,' &rt r-&q* , (b) (6 points) When Be"t (( B;rr1, the first order Zeeman correction to the energy level is given by E,t : peglB.*tmj where \$: {1 + U0+1) - S(0+1) + s(s+ 1 )]/[2j (l+ 1 )] ] . For the 3 s state, how many states are there due to the Zeeman correction? Calculate the energy difference between the states. If lru : 5.788x 10-s eV/T and Bext : 1 T, obtain a numerical value for the energy difference. 3s I 7L-- .(- -- ,t> s lx / j O (= L )-Lt o%t"i *(;) ,*| "z= 2-o: l+ > (*) (+) : +! s ! s .* a J :- /s\ , vli B 24t* j= t- t,-l rt l* L\ * t t /r8** AE e -/e B*rr- I+ -v lr?
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