I am trying to find the matrix representing a modified Stern-Gerlach apparatus (as proposed in the Feynman lectures) with its magnetic field in the z direction and a filter that blocks spin 1/2 atoms that are in the |-z> state (thus I'll call the apparatus a SG+z apparatus). I want to use |+x> and |-x> as base states.(adsbygoogle = window.adsbygoogle || []).push({});

For an atom in the |+y> = 0,707|+x> + 0,707|-x> state entering the SG+z apparatus to exit in the |+z> = 0,707|+x> + 0,707 i |-x> state, the apparatus would have to correspond to the matrix $$\left( \begin{array}{cc} 1 & 0 \\ i & 0 \end{array} \right)$$.

The same matrix will transform the states |-y> = 0,707|+x> - 0,707|-x>, |+z>, |-z> = 0,707|+x> - 0,707 i |-x> and |+x> into the state |+z> as required, but it doesn't work for the state |-x> (it gives 0!). Am I trying to do something that is impossible or incorrect here?

I am aware my question might need some clarification, which I will be happy to provide.

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# Matrix for a Stern-Gerlach apparatus

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