A problem of interacting charge carriers confined in quasi-one-dimensional ͑1D͒ semiconductor nanostructures has been studied. We have derived an analytical 1D formula for the effective interaction potential between the confined charge carriers. We have applied both the 1D model with the effective potential and the full three-dimensional ͑3D͒ approach to an electron pair confined in a single and double quantum dot as well as to an exciton confined in a quantum wire. Comparing the results of the 1D and 3D approaches we have discussed the applicability of the effective 1D interaction potential to the real 3D nanostructures. We have shown that the present effective interaction leads to accurate results for weakly coupled multiple quantum dots and wire-like nanostructures, i.e., the quantum wires and dots with the lateral confinement much stronger than the longitudinal one.

We study the Stark effect for an exciton confined in a pair of vertically coupled quantum dots. A single-band approximation for the hole and a parabolic lateral confinement potential are adopted which allows for the separation of the lateral center-of-mass motion and consequently for an exact numerical solution of the Schrödinger equation. We show that for intermediate tunnel coupling the external electric field leads to the dissociation of the exciton via an avoided crossing of bright and dark exciton energy levels which results in an atypical form of the Stark shift. The electric-fieldinduced dissociation of the negative trion is studied using the approximation of frozen lateral degrees of freedom. It is shown that in a symmetric system of coupled dots the trion is more stable against dissociation than the exciton. For an asymmetric system of coupled dots the trion dissociation is accompanied by a positive curvature of the recombination energy line as a function of the electric field.

Few-electron systems confined in quasi one-dimensional quantum dots are studied by the configuration interaction approach. We consider the parity symmetry of states forming Wigner molecules in large quantum dots and find that for the spin-polarized Wigner molecules it strictly depends on the number of electrons. We investigate the spatial spin-ordering in the inner coordinates of the quantum system and conclude that for small dots it has a short-range character and results mainly from the Pauli exclusion principle while the Wigner crystallization in large dots is accompanied by spin ordering over the entire length of the dot.