Measuring the Probability Density of Quantum Confined States

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In order to analyze the effect of electron-electron interaction on measuring the probability density of quantum confined states, a computer program has been made which numerically calculates the exact N-electron states in a quantum dot by diagonalizing the Hamiltonian matrix.Electronic structures in circular, elliptic and triangular shaped quantum dots containing single or N electrons have then been calculated using the computer program. In a circular quantum dot, the addition energy shows a clear structure as a function of N due to the shell filling and the spin polarized half filling. In an elliptic quantum dot, however, the structure is found to be diminished, which is attributed to the splitting of the degenerated single-particle states due to the asymmetric confining potential. Tunneling matrix elements through a quantum dot have been calculated by using the eigen states evaluated with the exact diagonalization.Energy relaxation time through longitudinal-acoustic phonon emission has also been calculated for a GaAs quantum dot with N electrons (from N=1 to 4), where the electrons in a narrow quantum well are confined by a parabolic confining potential. The electronic states are numerically evaluated by taking into account of the Coulomb interaction between the electrons, and the relaxation time is estimated by using the Fermi's golden rule. As the number of electrons increases, the energy levels become dense, and the number of relaxation channels drastically increases. From the evaluation of the relaxation time associated with all the relaxation channels, several relaxation processes are found to be accelerated by indirect process through some intermediate states between the initial and the final states.