  We study the statics and dynamics of a stable, mobile, three-dimensional
matter-wave spherical quantum ball created in the presence of an attractive
two-body and a very small repulsive three-body interaction. The quantum ball
can propagate with a constant velocity in any direction in free space and its
stability under a small perturbation is established numerically and
variationally. In frontal head-on and angular collisions at large velocities
two quantum balls behave like quantum solitons. Such collision is found to be
quasi elastic and the quantum balls emerge after collision without any change
of direction of motion and velocity and with practically no deformation in
shape. When reflected by a hard impenetrable plane, the quantum ball bounces
off like a wave obeying the law of reflection without any change of shape or
speed. However, in a collision at small velocities two quantum balls coalesce
to form a larger ball which we call a quantum-ball breather. We point out the
similarity and difference between the collision of two quantum and classical
balls. The present study is based on an analytic variational approximation and
a full numerical solution of the mean-field Gross-Pitaevskii equation using the
parameters of $^7$Li atoms.
