The raising and lowering angular momentum operators, J-hat(subscript +), J-hat(subscript -) are defined in terms of the Cartesian components J-hat(subscript x), J-hat(subscript y), J-hat(subscript z) of angular momentum J-hat by J-hat(+)=J-hat(x)+iJ-hat(y) and J-hat(-)=J-hat(x)-iJ-hat(y).
Obtain the matrix representation of J(subscript y) for the state with j=1 in terms of the set of eigenstates of J-hat(subscript z).
The Attempt at a Solution
J(subscript y)=(-i/2) (0 sqrt 2 0)
(-sqrt 2 0 sqrt 2)
(0 -sqrt 2 0)
I don't know why though. And what does it mean why 'in terms of the set of eigenstates J-hat(z)?