For S = 2, I have the following hamiltonian,(adsbygoogle = window.adsbygoogle || []).push({});

[tex] H=a \left( 2\,{S}^{2}-4\,{S_{{z}}}^{2} \right) +4\,b \left( (\left { S_+}^{3}) +({S_-}^{3})

[/tex]

I'm to show that a rotation of 180º,

[tex]e^{-i \pi S_x/ \hbar}[/tex]

leaves the hamiltonian unchanged.

I started thinking I could use the baker-hausdorff formula, but now not so sure - you would get something like, H + commutation terms. The first would be obvious zero, [Sx, S^2], but the other ones get messy.

Is the way to do this to find the matrix rep for Sx, S+, S-, then you would have the hamiltonian in matrix rep, along with the operator, and then do the series expansion for the exp?

I guess this would satisfy another part to this quesiton, which is to get the rep for Dm'm matrix. But it seems to me that one should be able to answer the first part without directly calculating the matrix?

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# Homework Help: Spin-2 system & rotation

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