Show that the spherical harmonics where ψ is a solution to the scalar wave equation are solutions to the vector wave equ

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answerhappygod
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Show that the spherical harmonics where ψ is a solution to the scalar wave equation are solutions to the vector wave equ

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Show that the spherical harmonics
 1
1 (2.53 KiB) Viewed 16 times
where ψ is a solution to the scalar wave equation
 2
2 (1.59 KiB) Viewed 16 times
are solutions to the vector wave equation. (This fact means that the problem of finding solutions to the vector wave equation reduces the problem much easier to find solutions to the scalar wave equation.)
PLEASE WRITE THE STEP BY STEP WITH ALL THE ALGEBRA. I NEED A DETAILED AND COMPLETE DEMOSTRATION TO UPVOTE.
м M = V x (70) 1 Ex M, V M, k 12 Ñ =
v28 +kv = 0,
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