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## Homework Statement

[S

^{2}

_{total}, S

_{z}∅1]

## Homework Equations

S

^{2}

_{total}= S

^{2}∅1+ 1∅S

^{2}+2(S

_{x}∅S

_{x}+S

_{y}∅S

_{y}+ S

_{z}∅S

_{z})

## The Attempt at a Solution

I calculated it in steps:

(1∅S

_{x}

^{2}+S

_{x}

^{2}∅1) * S

_{z}∅1

=[S

^{2}

_{x}, S

_{z}] ∅1 + S

_{z}∅S

_{x}

^{2}

=-h_cut i (S

_{x}S

_{y}+S

_{y}S

_{x})∅1 + S

_{z}∅S

_{x}

^{2}

Is it correct way of doing it? I mean I just did one small segment of it. There is still a lot of calculation to be done. Is there any short method?