4. If the general angular momentum quantum number j is 1 there is a triplet of |j, mj) states 1,1, 1,0), and 1,-1) In this case a matrix representation for the operators J, Jj and J, can be construct...
4. If the general angular momentum quantum number j is 1 there is a triplet of |j, mj) states 1,1, 1,0), and 1,-1) In this case a matrix representation for the operators J, Jj and J, can be constructed if we represent the lj,m,) triplet by three component column vectors as follows 0 0 0 0 0 Jz can then be represented by the matrix: 00 1 (a) Construct matrix representations for the raising and lowering operators, J and J acting on the eigenstates |1, 1), |1,0), and |1, -1) in the representation given in equa- tion (4.1) (b) Use the relationships 2i to construct matrix representations for Jz and Jy. (c) Show that the matrix representations of J, J, and J, obey the commutation relation
4. If the general angular momentum quantum number j is 1 there is a triplet of |j, mj) states 1,1, 1,0), and 1,-1) In this case a matrix representation for the operators J, Jj and J, can be constructed if we represent the lj,m,) triplet by three component column vectors as follows 0 0 0 0 0 Jz can then be represented by the matrix: 00 1 (a) Construct matrix representations for the raising and lowering operators, J and J acting on the eigenstates |1, 1), |1,0), and |1, -1) in the representation given in equa- tion (4.1) (b) Use the relationships 2i to construct matrix representations for Jz and Jy. (c) Show that the matrix representations of J, J, and J, obey the commutation relation