Electronic states in quantum dots: effects of symmetry of the confining potential

N-electron eigenstates in circular, elliptic, and triangular shaped quantum dots (QDs) are calculated by numerically diagonalizing the N-particle Hamiltonian. In a circular QD, the addition energy exhibits large values for N=2 and 6 due to the complete shell filling, and shows slightly large values for N=4 and 9 which corresponds to a spin-polarized half filling shell structure with the total spin of S=h (spin-triplet state) and S=3h/2 (spin-quadruplet state), respectively. In elliptic QDs, the degeneracy of the single-particle states is removed, resulting in a transition of the ground state from the spin-polarized half filling configuration to the spin singlet state for a QD containing four electrons. The states with 3, 6, and 9 electrons in a triangular QD are found to be slightly more stable compared to a circular QD, which is interpreted in terms of a geometrical effect