The spin' function of a free particle, in the basis in which s_z is diagonal can be written as \[\left[ {\begin{array}{*{20}{c}} 1 \\ 0 \end{array}} \right]\] and \[\left[ {\begin{array}{*{20}{c}} 0 \\ 1 \end{array}} \right]\] with eigen values \[ + \frac{\hbar }{2}\] and \[ - \frac{\hbar }{2}\] respectively. In the given basis, the normalized eigen function of s_y with eigen value \[ - \frac{\hbar }{2}\] is

A. \[\frac{1}{{\sqrt 2 }}\left[ {\begin{array}{*{20}{c}} 1 \\ i \end{array}} \right]\]

B. \[\frac{1}{{\sqrt 2 }}\left[ {\begin{array}{*{20}{c}} 0 \\ i \end{array}} \right]\]

C. \[\frac{1}{{\sqrt 2 }}\left[ {\begin{array}{*{20}{c}} i \\ 0 \end{array}} \right]\]

D. \[\frac{1}{{\sqrt 2 }}\left[ {\begin{array}{*{20}{c}} i \\ 1 \end{array}} \right]\]

Answer: Option C