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: Coulomb gauge and scalar potential

  1. Jun 1, 2010 #1
    Hi there,
    I'm studying the interaction of one electron atom with an electromagnetic field. In every textbook the starting point is the hamiltonian of the system containing the scalar potential and the vector potential. But then the scalar potential is ignored and I don't understand why.
    I've read that in the coulomb gauge I can choose the scalar potential to be 0, why??
  2. jcsd
  3. Jun 2, 2010 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    In electromagnetism, you're allowed to perform the gauge transformation

    [tex]\textbf{A} \rightarrow \textbf{A}'= \textbf{A}+\nabla\lambda[/tex]

    [tex]\Phi \rightarrow \Phi'= \Phi - \partial_t \lambda[/tex]

    The situation you're describing is a combination of the Lorenz and Coulomb gauges. In the Lorenz gauge, you have

    [tex]-\partial_t \Phi + \nabla \cdot \textbf{A} = 0[/tex]

    The Lorenz gauge is only a partial gauge fixing, so you still have the freedom to do an additional gauge transformation. In particular, if you choose the gauge function λ such that

    [tex]\Phi = \partial_t \lambda[/tex]

    you will have, after the gauge transformation, [itex]\Phi' = 0[/itex] and [itex]\nabla\cdot\textbf{A}'=0[/itex], which is the Coulomb gauge.
  4. Jun 2, 2010 #3
    Thank you!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook