  The one-dimensional (1D) $t-J$ model is investigated using the density matrix
renormalization group (DMRG) method. We report for the first time a
generalization of the DMRG method to the case of arbitrary band filling and
prove a theorem with respect to the reduced density matrix that accelerates the
numerical computation. Lastly, using the extended DMRG method, we present the
ground state electron momentum distribution, spin and charge correlation
functions. The $3k_F$ anomaly of the momentum distribution function first
discussed by Ogata and Shiba is shown to disappear as $J$ increases. We also
argue that there exists a density-independent $J_c$ beyond which the system
becomes an electron solid.
