Exercise $5\mathrm{.}10$

Consider the operator A$1$

$2$ J

x J

y J

y J

x $.$

$($a$)$ Calculate the expectation value of A$$ and A

$2$ with respect to the state j mO$.$

$($b$)$ Use the result of $($a$)$ to find an expression for A

$2$ in terms of:

J

; $4,$

J

;$2,$ J$2$

z $,$ J$4$

$,$ J$4$

$.$