  We report on a detailed examination of numerical results and analytical
calculations devoted to a study of two holes doped into a two-dimensional,
square lattice described by the t-J model. Our exact diagonalization numerical
results represent the first solution of the exact ground state of 2 holes in a
32-site lattice. Using this wave function, we have calculated several important
correlation functions, notably the electron momentum distribution function and
the hole-hole spatial correlation function. Further, by studying similar
quantities on smaller lattices, we have managed to perform a finite-size
scaling analysis. We have augmented this work by endeavouring to compare these
results to the predictions of analytical work for two holes moving in an
infinite lattice. This analysis relies on the canonical transformation approach
formulated recently for the t-J model. From this comparison we find excellent
correspondence between our numerical data and our analytical calculations. We
believe that this agreement is an important step helping to justify the
quasiparticle Hamiltonian, and in particular, the quasiparticle interactions,
that result from the canonical transformation approach. Also, the analytical
work allows us to critique the finite-size scaling ansatzes used in our
analysis of the numerical data. One important feature that we can infer from
this successful comparison involves the role of higher harmonics in the
two-particle, d-wave symmetry bound state -- the conventional (\cos(k_x) -
\cos(k_y)) term is only one of many important contributions to the d-wave
symmetry pair wave function.
