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!

Symmetries and Maxwells equations

  1. Dec 3, 2011 #1
    Hi

    Maxwells Equations for a time-invariant system are separable, hence we can write a solution as E(r, t) = E(r)E(t). They also mention that if the system is radially invariant, then that implies that the solution splits into a product of radial and angular functions (with 2π periodic angular functions).

    Is it a general rule that when the system described by Maxwells equations has a symmetry, then the solutions become separable? If yes, does this go beyond Maxwells Equations?

    Best,
    Niles.
     
  2. jcsd
  3. Dec 3, 2011 #2

    Vanadium 50

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor

    No. It's only true for 1/r and r2 potentials.
     
  4. Dec 3, 2011 #3
    Thanks. Where does that spatial dependence come into play when looking at Maxwells Equations? Is in through ε(r)=n(r)2?

    Do you have a suggestion for a reference that explains this in more details?

    Best,
    Niles.
     
  5. Dec 3, 2011 #4

    Vanadium 50

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor

    It's described in Volume 1 of Landau's Mechanics. Mathematically, it's because there is a hidden SO(4) symmetry in the equations describing the 1/r potential, and this symmetry (the same one that gives the n-l degeneracy in the hydrogen atom) ensures that the angular piece is separated out.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Symmetries and Maxwells equations
  1. Maxwell equations (Replies: 6)

  2. Maxwell equations (Replies: 4)

  3. Maxwell equation (Replies: 1)

  4. Maxwells equation (Replies: 1)

Loading...