Exact wave functions in a noncommutative field theory

We consider the nonrelativistic held theory with a quartic interaction on a noncommutative plane and compute the 2 --> 2 scattering amplitude within perturbative analysis to all orders. We regain the results of the perturbative analysis by finding the scattering and the bound state wave functions of the two particle Schrodinger equation. These wave functions unusually have two center positions in the relative coordinates, whose separation is transverse to the total momentum and scales linearly with its magnitude, exhibiting the stringy nature of the noncommutative field theory.