Sunday, 14 April 2019

mathematical physics - What restrictions on time boundary conditions does it have to use Fourier transform to solve wave equation?


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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