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07_751_Midterm_II

# 07_751_Midterm_II - Physics 751 Midterm II 16 November 2007...

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Physics 751 Midterm II 16 November 2007 This is a pledged midterm : you must not use stored information, paper or electronic, or communicate with anyone concerning the questions during the exam. Answer only three of the questions . If you attempt all four, make clear which one should not be graded, otherwise only the first three attempted will be graded. The partial credit assigned to parts of questions is shown thus: (5) . ______________________________________________________________________________ Possibly Useful Info: , | 1| 1 2 m p a x i a n n n m     2 2 [ , ] , | ( 1)| , | ( 1) ( 1) | , 1 i j ijk k x y J J i J J jm j j jm J J iJ J jm j j m m j m       ______________________________________________________________________________ 1. (5) (a) A simple harmonic oscillator is in the ground state 0 . What is the expectation value 4 x ? (5) (b) A simple harmonic oscillator is in the state 1/ 2 0 1 . Find the expectation value of 3 x , including time dependence. 2. (5) (a) Assuming p , x obey canonical commutation relations, find the commutation relations for the simple harmonic oscillator raising and lowering operators.

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07_751_Midterm_II - Physics 751 Midterm II 16 November 2007...

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