  We derive $q$-versions of Green's theorem from the Leibniz rules of partial
derivatives for the $q$-deformed Euclidean space. Using these results and the
Schr\"{o}dinger equations for a $q$-deformed nonrelativistic particle, we
derive continuity equations for the probability density, the energy density,
and the momentum density of a $q$-deformed nonrelativistic particle.
