This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 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 = 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 . Problem 2 (20 points): Quarks and antiquarks 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 antiquark bind together to form a meson (such as a πmeson). 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)...
View
Full
Document
This note was uploaded on 05/29/2011 for the course PHY 3063 taught by Professor Field during the Spring '07 term at University of Florida.
 Spring '07
 Field
 Physics

Click to edit the document details