  By introducing a boundary condition for the quantum wire, the Hubbard model
is solved exactly by means of Bethe ansatz. The wave function for the bounded
state is clearly defined, and the secular equation for the spectrum is exactly
obtained. The ground state and low-lying excited states are studied in the
thermodynamic limit. The ground-state energy in the strong coupling limit is
obtained explicitly, and compared with the results of periodic boundary
condition.
