1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
    2017 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!!
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted