- #1
Higgsono
- 93
- 4
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.
\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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