Quantum Monte Carlo investigations of quantum dots

In this thesis, we have applied both the Variational Monte Carlo (VMC) and Monte Carlo Diagonalization (MCD) techniques for calculation the ground-state energies of correlated electron-hole pair (exciton) and interacting two electrons confined in a two dimensional (2D) disc-like and three dimensional (3D) spherical parabolic quantum dots. The effects of dimensionality and quantum confinement on the ground state as well as binding energies of a correlated electron-hole pair in parabolic quantum dots have been investigated. 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. This study indicates that Monte Carlo Diagonalization technique combined with the trial wave function proposed as the harmonic-oscillator basis multiplied by correlation part in terms of Hylleraas-like coordinates are a powerful tool for studying interacting particles in parabolic quantum dots.