标题： 二维中的新关联：两体问题 显示英文标题

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

摘要： 我们讨论了Murthy、Bhaduri和Sen最近引入的二维多体哈密顿量，该哈密顿量包含两体和三体相互作用。除了分析多体系统中的一些精确解外，我们详细分析了完全可解的两体问题。 我们表明，两体问题的解归结为求解一个由Heun提出的已知微分方程。 我们表明，对于较大的相互作用强度，两体谱变得非常简单，并且能级结构类似于朗道能级。 我们还澄清了定义逆平方势所需的“紫外”正则化，并讨论了它对我们模型的影响。 显示英文摘要

摘要： 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.