  The one-dimensional (1D) $t$-$J$ model is investigated by using a
Gutzwiller-Jastrow-type variation method and the exact diagonalization of small
systems. Variational expectation values are estimated by the variational Monte
Carlo method with sufficient accuracy. First, we represent the diagonalization
results. Physical quantities like momentum distribution and some correlation
functions show some behaviors which are not expected in repulsive models, as
the value of $J/t$ increases. These properties as well as energy are well
understood by introducing intersite correlation factors into wave functions.
The phase transition to a separated phase in large-$J/t$ region can be
described by an attractive Jastrow wave function in quantitative agreement with
the exact results. On the other hand, for the supersymmetric case ($J/t=2$) the
original Gutzwiller wave function becomes an extremely good trial function for
all the range of electron density. Here a kind of \lq\lq free electron" state
is realized, particularly in the low electron density. Next, the above wave
functions are compared with the Tomonaga-Luttinger-liquid-type wave function
proposed by Hellberg and Mele. It is found that the correlation factors in
short distances control bulk quantities like energy and the magnitude of
correlation functions, while the long-range part of correlataion factors
determines the critical behavior of correlation functions. Lastly, using these
functions, charge and spin susceptibilities and magnetization curve are
estimated, which agree with the exact results. It is shown that the Mott
transition in 1D $t$-$J$ model is quite different from the Brinkman-Rice
transition.
