NOVEL CORRELATIONS IN 2 DIMENSIONS - 2-BODY PROBLEM

We discuss a many-body Hamiltonian with two- and three-body interactio ns in two dimensions introduced recently by Murthy, Bhaduri and Sen. A part from an analysis of some exact solutions in the many-body system, we analyse in detail the two-body problem which is completely solvabl e. We show that the solution of the two-body problem reduces to solvin g a known differential equation due to Heun. We show that the two-body spectrum becomes remarkably simple for large interaction strengths an d the level structure resembles that of the Landau levels. We also cla rify the 'ultraviolet' regularization which is needed to define an inv erse-square potential properly and discuss its implications for our mo del.