[tex]\left(\begin{array}{cc}\grave{\psi_{x}}\\\grave{\psi_{y}}\end{array}\right)=(\left(\begin{array}{cc}1 & 0\\0 & 1\end{array}\right)-\frac{ie_{z}}{h}\left(\begin{array}{cc}L_{z} & 0\\0 & L_{z}\end{array}\right)-\frac{ie_{z}}{h}\left(\begin{array}{cc}0 & -ih\\ih & 0\end{array}\right))\left(\begin{array}{cc}\psi_{x}\\\psi_{y}\end{array}\right)[/tex](adsbygoogle = window.adsbygoogle || []).push({});

According to my book, the right hand side rotates a vector wave-function (psi_x and psi_y are both scalar functions of x and y) counterclockwise about the z axis by e_z. It seems to me that this must be a typo, and that instead, if you combine the first two matrices into a single operator L, and call the last matrix the operator S, then the transformation should be given by: J=L+SL, instead of J=L+S. I'm confused. thnx

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# Vector wave-function spin

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