We study the low energy effective theory describing the dynamics of D-
particles. This corresponds to the quantum-mechanical system obtained
by dimensional reduction of (9 + 1)-dimensional supersymmetric Yang-Mi
lls theory to 0 + 1 dimensions and can be interpreted as the nonrelati
vistic limit of the Born-Infeld action. We study the system of two lik
e-charged D-particles and find evidence for the existence of non-BPS s
tates whose mass grows like lambda(1/3) over the BPS mass. We give a s
tring interpretation of this phenomenon in terms of a linear potential
generated by strings stretching from the two D-particles. Some commen
ts on the possible relations to black hole entropy and eleven-dimensio
nal supergravity are also given.