Symmetries and Maxwells equations

  • Thread starter Niles
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  • #1
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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.
 

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  • #2
Vanadium 50
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No. It's only true for 1/r and r2 potentials.
 
  • #3
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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.
 
  • #4
Vanadium 50
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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.
 

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