Systematic studies of the transport properties in one type of low-dimensional semiconductor nanostructures, in which the motion of carriers is governed by quantum mechanics, are presented in this thesis. In addition, the electronic states in lowdimensional systems fabricated from GaAs / Al_𝑥Ga_1-𝑥As heterostructures have been investigated by using both transport methods and the static calculations.

The mode-matching technique and transfer-matrix method are employed to explore the motion of electrons in a double-bend quantum wire. The conductance of the quantum system is calculated as a function of Fermi energy. Special attentions have been paid to the resonant peaks in conductances at Fermi energies lower than the threshold energy of the lowest subband. The charge distributions and the current flows at these Fermi energies have also been visualized. The bound states in such classically unbound systems can be probed by the resonant peaks in the conductance. For a quantum wire with a multiple of double-bend discontinuities, miniband structures, related to the split bound states, have been investigated. Ananalytical expression is suggested to elucidate these features. Additionly, detailed investigations have been extended to thermal and nonlinear effects, and to the influence of geometrical shapes.

Many-body interactions, expected to play a great role in low-dimensional systems, have been considered. We have calculated the electronic states of a quantum wire with a cross section by density-functional theories. Results indicate that the energy cost for putting two electrons with opposite spins into one bound state is larger than the binding energy, i.e., one bound state can be occupied by only one electron.

Spin-density-functional theories are used to study the exchange effects and magnetic effects on the electronic states of an infinite quantum wire with an inplane magnetic field parallel to the wire. The intrinsic properties of the system have been given. The theories have further been applied to a quantum point contact in the one subband limit. The spin-dependent saddle potentials have been observed. The semi-classical Thomas-Fermi and related models have been examined for semiconductor systems of the kind considered in this thesis. It has been shown that these models are suitable for dealing with these systems qualitatively.