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3063_ProblemSet8 - PHY3063 Spring 2007 Problem Set 8 PHY...

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PHY3063 Spring 2007 Problem Set 8 Department of Physics Page 1 of 3 PHY 3063 Problem Set #8 Due Tuesday April 24 (in class) (Total Points = 105) Reading: Read Tipler & Llewellyn Chapter 7. Problem 1 (20 points): The Pauli spin matrices are given by = 0 1 1 0 x σ = 0 0 i i y σ = 1 0 0 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 . Problem 2 (20 points): Quarks and anti-quarks carry spin ½. (a) (10 points) Three quarks bind together to form a baryon (such as a proton or a neutron). What are the possible spin states for a baryon (assuming that the quarks are in the ground state so that the orbital angular momentum is zero). (b) (10 points) A quark and anti-quark bind together to form a meson (such as a π -meson). What are the possible spin states for a meson (assuming that the quarks are in the ground state so that the orbital angular momentum is zero). Problem 3 (10 points): Evaluate the following in SU(2). (a) (1 point) 2 × 1 = (b) (1 point) 2 × 2 = (c) (1 point) 3 × 2 = (d) (1 point) 3 × 3 = (e) (1 point) 5 × 2 = (f) (1 point) 5 × 3 = (g) (1 point) 4 × 2 = (h) (1 point) 2 × 2 × 2 = (i) (1 point) 2 × 2 × 3 = (j) (1 point) 3 × 3 × 3 =
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