  We study a nearest-neighbor hopping model on the Cayley tree under the smooth
boundary condition with the modulation function $f_s=\sin^2[\pi s/(2M+1)]$,
where $s$ is a distance from the central site, and $M$ is the number of shells
on the tree. As a result of this smoothing, the particle density in the ground
state becomes nearly uniform in the bulk region even when $M$ is relatively
small. We compare the calculated particle density at the center with exact
result on the Bethe lattice, and they show a good agreement. The calculated
bond energy at the center also agrees with that on the Bethe lattice.
