Dirac equation continuity issue

1. Mar 22, 2013

raymo39

So I definitely believe that the continuity of the Dirac equation holds, there is one thing that annoys me, which is that

$$c \alpha . (-i \hbar \nabla \psi ) = c (i \hbar \nabla \psi^\dagger ) . \alpha$$

from the first part of the Dirac Hamiltonian
because the momentum operator should be Hermitian, but there is clearly a change of sign. I realise that the Hermitian conjugate of the spinor is now differently oriented, but shouldn't there be a change in ∇ such that its hermitian adjoint is negative itself to preserve the Hermitian nature of p?
I'm quite happy to try and prove this myself, but im a bit lost as to where to start

Last edited: Mar 22, 2013
2. Mar 22, 2013

andrien

momentum operator is defined as in schrodinger one,i.e. p=-ih-∇,which is hermitian as everyone knows.