Question

I ONLY NEED HELP PARTS E AND F

2. Consider the spin representation with j = 2 (in units of h). The corresponding matrices are 110 1 21 122 0 -i i ols We define J2-J12 + J22 + J32, J+ = J1 + 1J2, and J-= J1-1J2. A) (1 point) Show that 12 equals the identity matrix times jG +1), where- B) (3 points) Show that aJbic Eabe Jc for each combination a, b 1, 2,3 C) (2 points) Show that U3J 1-and U3Л.-J+. D) (1 points) Let |m) be a properly normalized eigenvector of J3 witlh eigenvalue m. What are the possible values for m'? E) (2 points) Show that/d-lm)= (m-1).lm). F (2 points) From part E we can conclude that J-Im) is either zero or an eigenvector of Js with eigenvalue of m-1. Show that (m-Im)- j+1)-m2+m

Answer 1

The results requires simple manipulation of angular momentum algebra involving their commutation relations.

"(E) J_3 J_-