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Satisfying Dirac equation, how to make equal to zero.

  1. May 31, 2015 #1
    1. The problem statement, all variables and given/known data
    AZGM7km.jpg

    2. Relevant equations
    Dirac equation: $$(\gamma ^{\mu}\rho_{\mu}-mc)\psi=0$$

    3. The attempt at a solution
    If we multiply out the Dirac equation by inserting all it's componants we get:

    a8n4gLY.jpg

    which if I've multiplied it correctly gives $$
    \begin{bmatrix}
    \frac{E}{c}-mc\\ 0
    \\ \rho_{z}
    \\ \rho_{x}+i\rho_{y}

    \end{bmatrix}e^{-\frac{iEt}{\hbar}}=0$$

    I'm not sure how to show the left hand side is equal to zero?

    edit just realised that it is at rest so all the ##\rho## componants would be zero, but then I still dont see how E/c - mc multiplied by the exponential would give zero?

    Any help / ideas would really be appreciated.
     
  2. jcsd
  3. May 31, 2015 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    If the particle is at rest, what is its relation between energy and mass?
     
  4. May 31, 2015 #3
    ahhhh E=mc^2 so the term in the matrix would be zero, many thanks!!
     
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