Electronic structure of quantum dots

In this thesis, an efficient method for reducing the computational effort of variational calculations with Hylleraas-like wavefunctions is introduced. The method consists in introducing integral transforms for the terms as r_k^12 exp (?? r12)arising out from the explicitly correlated wavefunctions. Introduced integral transforms provide the calculation of expectation value of energy and the related matrix elements to be done analytically over single-particle coordinates instead of Hylleraas coordinates.We have applied the method to calculate the ground state energies of different types of two-particle systems (atomic systems and artificial atoms). The first application of the present method has been done on atomic two-particle systems. The ground state energies of helium and a few helium-like ions with nuclear charge Z = 1 ? 6 were computed by four-parameters wavefunction, satisfying the boundary conditions for coalescence points and combined with Hylleraas-like basis set. To further the investigation of the applicability of the method, we have studied the ground state energies of electron-hole pair and two electrons in zero-dimensional semiconductor systems. The effects of quantum confinement on the ground state energy of a correlated electron-hole pair in a spherical and in a disk-like quantum dot have been investigated as a function of quantum dot size. Moreover, under parabolic confinement potential and within effective mass approximation, size and shape effects of quantum dots on the ground state energy of two electrons have been studied.The results show that, the method proposed in this thesis provides powerful tool to obtain the ground state energy of two-particle systems. With a properly chosen trial wavefunctions, variational determination of the ground state energy of two-particle systems were achieved without time-consuming numerical calculations. The results of calculations even with a small number of basis sets are in good agreement with previous theoretical works given in literature.