p246finalsol06

p246finalsol06 - Physics 246, Spring 2006 Final Exam...

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Unformatted text preview: Physics 246, Spring 2006 Final Exam Monday, May 8, 2006 • Answer all questions, using the paper provided. Begin each problem on a sepa- rate sheet. The pages will be separated for grading, so clearly label the problem number and put your name on EACH PAGE. • One 8.5 by 11 inch cheat sheet (front and back) allowed. No other books, calculators or notes allowed. • SHOW ALL WORK. • This exam has 150 points total. • Potentially useful information: Z nπ (sin 2 θ ) dθ = Z nπ (cos 2 θ ) dθ = nπ 2 Z + ∞-∞ e ix ( k- k ) dx = 2 π δ ( k- k ) ˆ a † | n > = √ n + 1 | n + 1 > ˆ a | n > = √ n | n- 1 > L ± | l, m > = ¯ h [ l ( l + 1)- m ( m ± 1)] 1 / 2 | l, m ± 1 > Z + ∞-∞ e- y 2 dy = √ π 1 1. Short answer (15 points total). You do not need to explain your answers in this problem unless explicitly asked to do so. (a) (2 points) What are the units of ¯ h ? (b) (3 points) True or false? In time dependent perturbation theory, a per- turbation that depends on time can induce transitions between different states only if the perturbation also has some space dependence. Explain briefly . (c) (3 points) For each following operator, state whether it is Hermitian....
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p246finalsol06 - Physics 246, Spring 2006 Final Exam...

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