  We report on quantum Monte Carlo calculations of the ground and low-lying
excited states of $A=9,10$ nuclei using realistic Hamiltonians containing the
Argonne $v_{18}$ two-nucleon potential alone or with one of several
three-nucleon potentials, including Urbana IX and three of the new Illinois
models. The calculations begin with correlated many-body wave functions that
have an $\alpha$-like core and multiple p-shell nucleons, $LS$-coupled to the
appropriate $(J^{\pi};T)$ quantum numbers for the state of interest. After
optimization, these variational trial functions are used as input to a Green's
function Monte Carlo calculation of the energy, using a constrained path
algorithm. We find that the Hamiltonians that include Illinois three-nucleon
potentials reproduce ten states in $^9$Li, $^9$Be, $^{10}$Be, and $^{10}$B with
an rms deviation as little as 900 keV. In particular, we obtain the correct
3$^+$ ground state for $^{10}$B, whereas the Argonne $v_{18}$ alone or with
Urbana IX predicts a 1$^+$ ground state. In addition, we calculate isovector
and isotensor energy differences, electromagnetic moments, and one- and
two-body density distributions.
