Interacting electrons in one-dimensional confinements

We study the ground state energy/properties of a system of interacting electrons confined one-dimensionally, with the aid of the Bethe ansatz method. We first derive a set of fundamental equations, explicitly taking into account the confinement of the system. We then obtain the numerical solution of this set of fundamental equations to determine the ground state energy/properties for a few electrons in the system. On the basis of the obtained results, we discuss the effects of the confinement and the electron–electron interaction on the ground state properties of the system of interacting electrons confined in one-dimension, comparing the results with those for a system of interacting electrons with periodic boundaries.