Welcome Guest!
For persistent fullscreen mode, use F11 function key.

# Problem/QM-06010

For page specific messages
For page specific messages

The vector space needed to describe a particular physical system is two
dimensional complex vector space. The  states are therefore represented by 2
component complex column vectors. The observables for this system are $2\times2$
matrices. A set of three dynamical variables of the system, $X,Y,Z,$ are be
represented by $2\times 2$ matrices denoted by $\sigma_x, \sigma_y,\sigma_z$,
where  $$\sigma_x =\begin{pmatrix}0&1\\1&0\end{pmatrix},\qquad \sigma_y=\begin{pmatrix} 0&-i\\i&0\end{pmatrix}, \qquad \sigma_z=\begin{pmatrix}1&0\\0&-1\end{pmatrix}.$$     What values are
experimentally allowed if one measures the dynamical variable

1.        $X$
2.       $Z$
3.       $T= X^2+Y^2+Z^2$

n