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A vector potential $A(x, t)$ satisfies the wave equation $\left(\Delta-\frac{1}{c^2}\frac{\partial^2}{\partial t^2}\right) A(x, t)=0$.

It is written in my physics textbook that the general solution of the wave function is superposition of $e^{(1)}a_k e^{i(k\cdot x-\omega t)}$.

How to prove there are no other solutions?

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marked as duplicate by BCLC, Community Jul 28 '18 at 9:47

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