Question

(a) Obtain the angular momentum matrices for j = 1 

(b) Hence obtain the matrix for J².

Answer 1

(a) For j = 1, m = 1, 0 and −1, the three base states are denoted by |1 >, |2 > and |3 >. In the | j, m > notation |1 >= |1, 1 >, |2 >= |1, 0 >, |3 >= |1, −1 >

By a similar procedure the matrix elements of J_y can be found out. Thus