Problem $4\mathrm{.}30$ An electron is in the spin state $2,$ ed $3$i X$=$A at $($a$)$ Determine the normalization constant A$.($b$)$ Find the expectation values of Se$,$ Sy$,$ and S $($c$)$ Find the "uncertainties" os$,,$ as$,,$ and as$,.$ Note: These sigmas are standard u$-$ or re or deviations, not Pauli matrices! $2).($d$)$ Confirm that your results are consistent with all three uncertainty principles $($Equation $4\mathrm{.}100$ and its cyclic permutations$-$only with S in place of L$,$ of course$).$ ng ely X$-$ Notice that Ly$,$ Ly$,$ and L$,$ are incompatible observables. According to the generalized uncertainty principle $($Equation $3\mathrm{.}62),2$ h$2($ihL;$)$ or $(4\mathrm{.}100)$ OL$,$aL$,$ L:$)$ It would therefore be futile to look for states that are simultaneously eigenfunctions of Ly and Ly$.$On the other hand, the square of the total angular momentum, $(4\mathrm{.}101)$ does commute with Lx: L$.$L$.]-[$Li$.$ L$.]+[3,$ L$.]+=$Ly $[$Ly$.$ Lx$]+[$Ly$.$ L$.]$ Ly $+$ L $[$Lz$,$ Lx$]+[$Lr$,$ Lx$]$ L $=$ Ly $(-$ihL,$)+(-$ihL.$)$ Ly $+$ L $($ihL$,)+($ihLy$)$ L $=0.$