Theoretical studies in condensed matter physics: A. Correlation energies and wavefunctions for two interacting electrons in a harmonic quantum dot. B. Equivalent Hamiltonian without effective-mass approximation

This thesis is divided into two parts. The first part, "Correlation Energies and Wave-functions for Two Interacting Electrons in a Harmonic Quantum Dot", provides a new method to obtain the analytical form of both the energy levels as well as the wavefunctions for two interacting electrons in such a dot. They are based on a double-parabola approximation in the WKB framework. A separate variational approach has to be used for the ground state since the previous method is not applicable. The correlation manifests itself not only as energy corrections but more interestingly, also in the spatial displacement of the relative wavefunction as the ratio of Coulomb repulsion to the confining potential varies. Such information could be incorporated, for example, into the dieletric function of these systems and might be verifiable in electron scattering experiments.; The second part, "Effective Hamiltonian Without Effective-Mass Approximation", provides a possible way to calculate the subband splitting in a semiconductor under an external field when the bulk band-structure has two or more minima in the direction of the external field. The effective-mass approximation has to be replaced by the original effective Hamiltonian method in which the characteristics of the whole band structure are retained. Our purpose is to examine the effect of the entire band structure rather than the effect of one valley which can be considered through the effective-mass approximation. The saddle point method is applied to the boundary conditions to find the energy quantization.