The wave equation can be solved using Fourier transform, by assuming a solution of the form of $$\mathbf{E}(x,y,z,t)~=~\mathbf{E}(x,y,z)e^{j\omega t}$$ and then reducing the equation to the Helmholtz equation.
What are the presumed restrictions on the solution, when solving the equation this way? (e.g., on time boundary condition) I mean can this method give the most general solution (given some boundary conditions)? What features does the solution obtained this way have?
Does it have any difference with solutions obtained using Laplace transform? (The very same above questions, for Laplace transform.)
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