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

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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 0 (sin 2 θ ) = Z 0 (cos 2 θ ) = 2 Z + -∞ e ix ( k - k 0 ) dx = 2 π δ ( k - k 0 ) 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
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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. i. x ii. ∂/∂x iii. angular momentum raising operator (d) (2 points) In matrix mechanics, in a basis of energy eigenstates, what
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