- #1

- 287

- 0

Given [tex]S=\frac{1}{2}\hbar{\sigma} [/tex] where [tex]\sigma = \left(\left(\begin{array}{cc}0&1\\1&0\end{array}\right),\left(\begin{array}{cc}0&-i\\i&0\end{array}\right),\left(\begin{array}{cc}1&0\\0&-1\end{array}\right)\right) [/tex], show that

[tex] |+> = \left(\begin{array}{cc}1\\0\end{array}\right) [/tex] and [tex] |-> = \left(\begin{array}{cc}0\\1\end{array}\right) [/tex] are the eigenfunctions for [tex] S_z [/tex] . Obtain the matrix representation for [tex] S_y [/tex] and [tex] S_x [/tex] in the basis [tex] (|+>,|->)[/tex] .

[tex] |+> = \left(\begin{array}{cc}1\\0\end{array}\right) [/tex] and [tex] |-> = \left(\begin{array}{cc}0\\1\end{array}\right) [/tex] are the eigenfunctions for [tex] S_z [/tex] . Obtain the matrix representation for [tex] S_y [/tex] and [tex] S_x [/tex] in the basis [tex] (|+>,|->)[/tex] .

Last edited: