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The relationship between the spin operator matrices in
x,yand
zdirection with the Pauli matrices
\sigma _(x),\sigma _(y)and
\sigma _(z)are as the following respectively
[hat(S)_(x)]=(n)/(2)\sigma _(x),[hat(S)_(y)]=(n)/(2)\sigma _(y), and ,[hat(S)_(z)]=(n)/(2)\sigma _(z).Find the Pauli matrices a)
\sigma _(r), b)
\sigma _(y), c)
\sigma _()=