The possibility of describing quantum mechanical particles on a plane by a
Jastrow wave function is studied. We obtain the condition under which the
particles interact through pair potentials. It is found that if the
interparticle forces depend only on distance, then only the attractive harmonic
pair potential is consistent with the Jastrow ansatz. We discuss some
connections with wave functions encountered in the quantized Hall effect.Comment: 10 pages LaTeX, Phys. Lett. A to appea