(Solved): 4. Consider a rho meson with S=1 and L=2 (in a d orbital angular momentum state). We will specify ...

4. Consider a rho meson with $$\mathrm{S}=1$$ and $$\mathrm{L}=2$$ (in a $$\mathrm{d}$$ orbital angular momentum state). We will specify a specific state with $$m_L=1$$ and $$m_S=1$$. a) What are the possible values of $$\mathrm{J}$$ for this state? b) What are the possible values of $$m_J$$ for this state? c) Using the Clebsch-Gordan tables, express this state $$?\mathrm{LS}\mathrm{mL}\mathrm{mS}>=?21111>$$ in terms of $$?\mathrm{J}$$ mJ $$>$$ states. d) What are the possible results and the probability of each possible result for measurement of the following observables? i) $${\mathrm{J}}^2$$ ii) $${\mathrm{L}}^2$$ iii) $$L_z$$ iv) $$J_z$$ v) $$J_x^2+J_y^2$$