# I Hermitian operators

1. Nov 14, 2016

### Higgsono

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.

Last edited by a moderator: Nov 15, 2016
2. Nov 14, 2016

### blue_leaf77

$p$ acts on spatial part whereas $\alpha$ on spin part so the two operators commute.

3. Nov 14, 2016

ok, thanks!