# Hermitian operators

• I
In the dirac equation we have a term which is proportional to $$\alpha p$$. In the book they say that
$$\alpha$$ must be an hermitian operator in order for the Hamiltonian to be hermitian.

As I understand, we require this because we want $$(\alpha p)^\dagger = \alpha p$$.

But $$(\alpha p)^\dagger = p^\dagger \alpha^\dagger = p \alpha$$, and so the order of the operators still change.

So if we just require both operators to be hermitian their product will still change if we take the hermitian conjugate.

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blue_leaf77
Science Advisor
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##p## acts on spatial part whereas ##\alpha## on spin part so the two operators commute.

##p## acts on spatial part whereas ##alpha## on spin part so the two operators commute.
ok, thanks!