4604_ProblemSet6_fa07

4604_ProblemSet6_fa07 - PHY4604 Fall 2007 Problem Set 6...

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Unformatted text preview: PHY4604 Fall 2007 Problem Set 6 Department of Physics Page 1 of 2 PHY 4604 Problem Set #6 Due Wednesday November 14, 2007 (in class) (Total Points = 130, Late homework = 50%) Reading: Griffiths Chapter 4 Sections 4.4. Problem 1 (20 points): The Pauli spin matrices are given by = 1 1 x = i i y = 1 1 z (a) (10 points) Show that i = i , det( i ) = -1, Tr( i ) = 0, [ i , j ] = 2i ijk k , and { i , j } = 2 ij . Note that [A, B] = AB BA and {A, B} = AB +BA. (b) (10 points) Show that + = l l ijl ij j i i . ( Hint : see Griffiths section 4.3 and problem 4.26) Problem 2 (20 points): An electron is in the spin state >= 4 3 | i A . (a) (4 points) Determine the normalization constant A. (b) (8 points) Find the expectation value of S x , S y , and S z for the state | >, where r r h 2 = S ....
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4604_ProblemSet6_fa07 - PHY4604 Fall 2007 Problem Set 6...

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