[QUE/QM-06016]

\(\newcommand{\average}[2]{\rangle#1|#2|#1\rangle}\) The state of a quantum system is represented by a two component vector \[ f = \begin{pmatrix}1+3i \\3-i \end{pmatrix}\] For the dynamical variable \(Y\) \[Y = \begin{pmatrix}0 & -i\\i  & 0\end{pmatrix}\] compute the average $\average{f}{Y},\average{f}{Y^2} $  and the uncertainty $\Delta Y$ for the
variable $Y$ where \begin{equation*} Y= \begin{pmatrix} 0 & -i \\ i &0      
\end{pmatrix} \end{equation*} Give your remarks, if any, on the answer you obtained.