Suppose that you have a set of angular momentum operators j;i=1,2,3 that define an angular momentum j. A set of operators W; i = 1,2,3 is said to form a vector operator, w. if [3,w,]=iheyW. Note that J itself is a vector operator.
a. Show that when j is taken to be the orbital angular momentum, the position operator is a vector operator.
b. Show that if and are vector operators, so is the cross product x.
c. Show that if W is a vector operator, then [j^2,W]=2ih(Wxj-ihW).
d. Show that for a vector operator, the following formula holds [2,[3^2,v]-v.3j-3^2v+30] with a constant you must determine.