  An exactly solvable electron model of a confined system with inverse-square interaction is presented. The ground state is given by the Jastrow-product wavefunction of power-law form. We discuss the results in connection with conductance oscillations observed in semiconductor nanostructures, for which single-electron charging effects play a crucial role. Due to the internal spin degrees of freedom, there appear two independent periods of the conductance oscillations in very narrow channels even at zero temperature. 
Confined quantum systems in one dimension and conductance oscillations   in narrow channels