Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The dirac equation of the hydrogen atom

  1. Mar 3, 2013 #1
    What potential would one use when evaluating the Dirac equation of the hydrogen atom? Would it simply be in the form used when examining the hydrogen atom-Schrodinger equation or does it need modification?
  2. jcsd
  3. Mar 3, 2013 #2


    User Avatar
    Science Advisor

    In non-rel. QM one starts with the same 1/r potential. What else do you have in mind?
  4. Mar 3, 2013 #3
    I was just wondering that since the time-independent part of the solution is in vector form you might have to consider a potential in the form of a vector field. But maybe i´m wrong?
  5. Mar 3, 2013 #4
    Thanks for the reply by the way!
  6. Mar 3, 2013 #5


    User Avatar
    Science Advisor

    Choose a gauge in which the vector potential A = 0, leaving just the Coulomb 1/r potential. Separate variables in spherical coordinates as usual, and you'll find that the four components of the Dirac spinor can be written in terms of two radial functions, leding to recursion relations, etc, etc, and solved by confluent hypergeometric functions.
  7. Mar 3, 2013 #6
    Ill try that then. Thank you!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook