- #1
raymo39
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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 realize 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 I am a bit lost as to where to start
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 realize 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 I am a bit lost as to where to start
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