Fourier series method applied to different shaped quantum well laser potentials

Here we present a method using Fourier series representation of the potential to obtain the eigenvalues and eigenfunctions for a general isolated quantum well potential. We compare the method with analytical results in the case of a square well and get excellent agreement. Finally, we apply the method to two different graded-index, separate confinement heterostructure potentials of interest and compute the corresponding gain with k selection. We find the gain to be much narrower in energy range for multiple quantum wells as compared with a single quantum well