| Chapter one gives general introductions for quantum dots (QD). Chapter two studies two-dimensional (2D) QD-helium with magnetic fields ( B) by various theoretical approaches, focusing on the correlation effects. The eigenenergies and eigenfunctions are found from exact, variational, perturbational, quasi-classical (WKB) calculations, and their behaviors are studied as the confinement, electron-electron interaction, and B vary. The variational calculation reveals a possible existence of two different physical regimes. The WKB calculation reveals new, unexpected features of electron correlations, enabling the double-parabola, single-parabola approximations in the WKB regime. New spin-angular momentum-transitions with increasing interaction (or with decreasing confinement) at finite B, are found and discussed. A 3D QD-helium at B = 0 is studied and compared with the 2D one.;Chapter three studies a three-electron-2D-QD with B by the electronic molecule model, arguing that when the confinement is weak enough, the electron motions in QD are well-described quasi-classically, rather than by the conventional atomic picture. The total Hamiltonian is diagonalized by normal modes, using the group theory, to give full energy spectrum and eigenfunctions analytically. The total wavefunctions, including the spin part, are anti-symmetrized by purely group theoretical arguments. Only particular values of the total angular momentum are shown to be allowed for a given spin state. The physical origin of the magic number is identified. The model is justified self-consistently.;Chapter four calculates, using a perturbative-variational method, the ground state energies of D0, D - centers and binding energy of a D - center in a quantum well with B, as a function of B and a well width.;Chapter five calculates, first, the wave vector q and frequency o-dependent transverse dielectric function, eTq,w for a bulk semiconductor, showing that the reported calculations [61, 71] of eLq,0 and eTq,0 have mistakes that change the results both quantitatively and qualitatively. Some formerly unexplained behaviors of eTq,0 are explained. Using a model similar to the Penn model, eTq,w for a semiconductor film is calculated as a function of the film thickness and the energy (Penn) gap. It is found that unless q is quantized as the crystal momentum, the film becomes transparent eTq,w =1 , and that eTq,w increases with the film thickness. |
