  We formulate an effective Schroedinger wave equation describing the quantum
dynamics of a system of D0-branes by applying the Wilson renormalization group
equation to the worldsheet partition function of a deformed sigma-model
describing the system, which includes the quantum recoil due to the exchange of
string states between the individual D-particles. We arrive at an effective
Fokker-Planck equation for the probability density with diffusion coefficient
determined by the total kinetic energy of the recoiling system. We use Galilean
invariance of the system to show that there are three possible solutions of the
associated non-linear Schroedinger equation depending on the strength of the
open string interactions among the D-particles. When the open string energies
are small compared to the total kinetic energy of the system, the solutions are
governed by freely-propagating solitary waves. When the string coupling
constant reaches a dynamically determined critical value, the system is
described by minimal uncertainty wavepackets which describe the smearing of the
D-particle coordinates due to the distortion of the surrounding spacetime from
the string interactions. For strong string interactions, bound state solutions
exist with effective mass determined by an energy-dependent shift of the static
BPS mass of the D0-branes.
