If we have a hermitian operator Q and we know it's matrix representation [Q], does that mean that [Q(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}] = [Q]^{2}?

For example, I'm pretty sure that's the case for p^{2}for a harmonic oscillator. We have p=ic(a_{+}-a_{-}) and so

p^{2}=c^{2}(a_{+}-a_{-})(-a_{+}+a_{-})*=c^{2}(a_{+}-a_{-})(a_{+}-a_{-})=p p

Which tells us that [p^{2}]=[p]^{2}. But could we do that with any hermitian operator?

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# Square of a hermitian operator in matrix form

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