Application of Fourier transforms to find propagation constants of the localized modes symmetric planar waveguides. Analogies in the quantum mechanics

Numerical method of finding propagation constants of the localized modes of symmetric planar waveguides and solution of the stationary Schrödinger equation is developed. The method is based on Fourier transform of the wave equation and as result is obtained an integral equation in which the integral is replaced by summation. In of the final case, we obtain of linear algebra problem on the eigenvalues and eigenvectors. The method is tested on many examples.