  We show that the single quasi-particle Schr\"odinger equation for a certain
form of one-body potential yields a stationary one soliton solution. The
one-body potential is assumed to arise from the self- interacting charge
distribution with the singular kernel of the Calogero-Sutherland model. The
quasi-particle has negative or positive charge for negative or positive
coupling constant of the interaction. The magnitude of the charge is unity only
for the semion. It is also pointed out that for repulsive coupling, our
equation is mathematically the same as the steady-state Smoluchowski equation
of Dyson's Coulomb gas model.
