(Solved): Q.3 An angular momentum system with \( l=1 \) is prepared in the state \[ \psi=\frac{2}{\sqrt{29}} ...

Q.3 An angular momentum system with \( l=1 \) is prepared in the state \[ \psi=\frac{2}{\sqrt{29}} Y_{1}^{1}+i \frac{3}{\sqrt{29}} Y_{1}^{0}-\frac{4}{\sqrt{29}} Y_{1}^{-1} \] where \( Y_{l}^{m} \) are the eigenfunctions of the angular momentum operators \( L^{2} \) and \( L_{z} \). (a) What are the possible results of a measurement of the angular momentum observable \( L^{2} \) ? [1 mark] (b) What are the possible results of a measurement of the angular momentum component \( L_{z} \) ? [3 marks]