Mesh generation and electronic structure of quantum wires

In this thesis, single particle states in six different Quantum Wire cross-sectionsare studied by using Finite Element Method. In this case, energy values andcharge localizations are given with arbitrary confinement potential profiles suchas parabolic, linear and zero potentials. Mesh Generation which is necessary forthe Finite Element Analysis, is presented as a brief overview.This thesis also has detailed sections about the fundamental methods such asFinite Element Method, Area Coordinates, interpolation in d dimensions and thematrix elements of the generalized eigenvalue problem for the main problems.In additional to single particle states with arbitrary potential profiles, excitonstates in parabolic GaAs quantum dot is studied as a second problem. In thiscase, the energy spectrums of the exciton system versus confinement parameterand interaction parameter are showed in two energy scales. Because of the FEMis a powerful tool, the excited states are given with high accuracy in additional toground state which can be obtained by using the traditional variational methodsin the literature. Here again, charge localizations and the ground state energydata depending on quantum dot size has shown for different angular momentumquantum numbers.The result of the calculations are in perfect agreement with the analyticalsolutions of the well-known and principle problems which are mentioned in thefurther sections in this study.