1.4 Prove that the spherical harmonic wave function e^(ikr-wt) is a solution of the three-dimensional wave equation, where r = sqrt(x^2 + y^2 + z^2). The proof is easier if spherical coordinates are used.
Added by Paul D.
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It is given by: ∇²ψ = 1/c² ∂²ψ/∂t² where ∇² is the Laplacian operator in spherical coordinates, c is the speed of light, and ψ is the wave function. The Laplacian operator in spherical coordinates is given by: ∇² = 1/r² ∂/∂r (r² ∂/∂r) + 1/r²sinθ ∂/∂θ (sinθ Show more…
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