Let’s say you want to compute the spin angular momentum operators along the three Cartesian axes for single-spin Hilbert space
![\[ \hat{I}_x = \frac{1}{2}\left( \begin{matrix}0 & 1 \\ 1 & 0 \end{matrix}\right), \hat{I}_y = \frac{1}{2}\left( \begin{matrix}0 & -1 \\ +1 & 0 \end{matrix}\right), \hat{I}_z = \frac{1}{2}\left( \begin{matrix}+1 & 0 \\ 0 & -1 \end{matrix}\right).\]](https://quentinstern.com/wp-content/ql-cache/quicklatex.com-02c57961b091ed7e860424d95da666e1_l3.png "Rendered by QuickLaTeX.com")
The codes to generate them is
Ix=I(N,1,'x');
Iy=I(N,1,'y');
Iz=I(N,1,'z');
Equivalently, one may write
where the second argument specifies that the operator corresponds to Spin 1. As there’s only a single spin in the Hilbert space, the argument is not necessary.
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x=1;
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