This research is built upon the determination of the Eigenpairs of one and two dimensional positive differential operators with periodic boundary conditions. The Schrödinger equation was solved for positive operators in both one and two dimensions. Fourier series were used to express the derivatives as the summation of Fourier terms. This led to a novel approach for the calculation of the eigenmodels of a perturbed potential well. The perturbation can be done via an electric field applied to the potential well. The research in this thesis includes a thorough understanding of quantum mechanics fundamentals, mastering of different approximation techniques such as the variational technique and results that have been generated and published using the novel techniques. |
