4604_ProblemSet6 - PHY4604 Problem Set 6 Department of...

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Unformatted text preview: PHY4604 Problem Set 6 Department of Physics Page 1 of 2 PHY 4604 Problem Set #6 Due Monday November 13, 2006 (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 σ − = i i y σ − = 1 1 z σ (a) (10 points) Show that σ ↑ i = σ i , det( σ i ) = -1, Tr( σ i ) = 0, [ σ i , σ j ] = 2i ε ijk σ k , and { σ i , σ j } = 2 δ ij . Note that [A, B] = AB – BA and {A, B} = AB +BA. (b) (10 points) Show that ∑ + = l l ijl ij j i i σ ε δ σ σ . ( 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 χ . (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 | χ >, where σ r r h 2 = S ....
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This note was uploaded on 04/19/2008 for the course PHY 4604 taught by Professor Field during the Spring '07 term at University of Florida.

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4604_ProblemSet6 - PHY4604 Problem Set 6 Department of...

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