Two-component δ-function fermions and bethe ansatz eigenstates

Two-component repulsive δ-function fermion system is studied on an infinite interval. A basis set of the Bethe ansatz eigenstates is constructed, and its completeness and orthonormality are proved. The correspondences among these Bethe ansatz states, the states made by the quantum inverse scattering method, and the incoming (outgoing) states of the scattering theory are shown. This confirms the validity of the quantum Gelʹfand-Levitan equations for studying the thermodynamics of the system. In addition, thermodynamic quantities are evaluated by use of the complete set of the Bethe ansatz states and the first two terms of the virial expansions are explicitly shown.