Recently, the electron transport through a quasi-one dimensional (quasi-1D) electron gas was investigated experimentally as a function of the confining potential. We present a physical model for quantum ballistic transport of electrons through a short conduction channel, and investigate the role played by the Coulomb interaction in modifying the energy levels of twoelectron states at low temperatures as the width of the channel is increased. In this regime, the effect of the Coulomb interaction on the two-electron states has been shown to lead to four split energy levels, including two anticrossings and two crossinglevel states. Due to the interplay between the anticrossing and crossing of the energy levels, the ground state for the twoelectron model switches from one anticrossing state for strong confinement to a crossing state for intermediate confinement as the channel width is first increased, and then returned to its original anticrossing state. This switching behavior is related to the triplet spin degeneracy as well as the Coulomb repulsion and reflected in the ballistic conductance. Here, many-body effects can still affect electron occupations in the calculation of quantum ballistic conductance although it cannot vary the center-of-mass velocity.