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Dirac equation continuity issue

  1. Mar 22, 2013 #1
    So I definitely believe that the continuity of the Dirac equation holds, there is one thing that annoys me, which is that

    [tex] c \alpha . (-i \hbar \nabla \psi ) = c (i \hbar \nabla \psi^\dagger ) . \alpha [/tex]

    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. jcsd
  3. Mar 22, 2013 #2
    momentum operator is defined as in schrodinger one,i.e. p=-ih-∇,which is hermitian as everyone knows.
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