The momentum distribution function n(k) and spin-correlation function S(k) are determined for the one-dimensional large-U Hubbard model with various electron densities. The present work is featured with an application of the Bethe-ansatz wave function, which has a simple form in the large-U limit for any electron density. Namely, its charge degrees of freedom are expressed as a Slater determinant of spinless fermions, while its spin degrees of freedom are equivalent to the one-dimensional S=(1/2 Heisenberg model. The singularity of n(k) at k=
kF is analyzed from the system size dependence. In addition to the
kF singularity, n(k) has a weak singularity at k=3
kF; however, no detectable singularity is present at 2
kF, which one might expect from the spinless fermion wave function. The singularity of S(k) at 2
kF is also examined in detail. It is concluded from the size dependence that, when the system is away from half-filling, the nature of the singularity at 2
kF is different from that in the Heisenberg model. The results are compared with the behavior in the weak-correlation regime examined with the perturbation calculation, the prediction of g-ology, and recent Monte Carlo calculations.
The ``string'' structure of one-dimensional Hubbard model eigenstates is studied numerically and is used to suggest the validity of thermodynamic Bethe-ansatz equations (TBAE). We furthermore solve TBAE in a strong-coupling expansion series form and obtain the thermodynamic potential which agrees with the known high-temperature expansion series. We also calculate various thermodynamic quantities using our solution and provide some additional features of the strongly correlated one-dimensional Hubbard model.