Novel correlations in two dimensions: Two-body problem

Details Novel correlations in two dimensions: Two-body problem Novel correlations in two dimensions: Two-body problem

1996-09-02

arxiv.org/abs/cond-mat/9609012v1

J. Phys. A 30 (1997) 2557-2576

Physics

Condensed Matter

36 pages in revtex and 2 postcript figures

Scientific paper

10.1088/0305-4470/30/7/032

We discuss a many-body Hamiltonian with two- and three-body interactions in two dimensions introduced recently by Murthy, Bhaduri and Sen. Apart from an analysis of some exact solutions in the many-body system, we analyze in detail the two-body problem which is completely solvable. We show that the solution of the two-body problem reduces to solving a known differential equation due to Heun. We show that the two-body spectrum becomes remarkably simple for large interaction strength and the level structure resembles that of the Landau Levels. We also clarify the "ultraviolet" regularization which is needed to define an inverse-square potential properly and discuss its implications for our model.

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