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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.