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Klein-Gordon-Schrodinger and Dirac equations

  1. Sep 19, 2007 #1
    1. The problem statement, all variables and given/known data
    I need to solve the Klein-Gordon-Schrodinger and the Dirac equation for the Coulombian potential.

    2. Relevant equations

    [tex][(\partial^{\mu}\partial_{\mu} + m^2c^2/h^2)\Psi=0 [/tex]
    I don't know how I can add the potential term...

    [tex][\gamma^{\mu}(ih\partial_{\mu} - (e/c) A_{\mu})-mc)]\Psi=0 [/tex]

    3. The attempt at a solution

    I'm trying to do something with these equations in order to make them with a Schrodinger-like form. For the Dirac eq., I found the hydrogen atom resolved in Sakurai's book, but I could not understand what they did (they took about 10 pages) and I wonder if there is another (easier) way to do this.
    Last edited: Sep 19, 2007
  2. jcsd
  3. Sep 19, 2007 #2


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    There really isn't anu other way. A book solving both equations for the Coulomb potential is Greiner's "Relativistic Quantum Mechanics - Wave equations".
  4. Sep 19, 2007 #3
    Thanks. I'll look for this book online, 'cos I don't have it... :(
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