用so（2，1）李代数求解平面上的散射和束缚态格林函数
Scattering and Bound State Green's Functions on a Plane via so(2,1) Lie Algebra
摘要：
我们计算了粒子涡旋系统的格林函数，平面上有和没有谐波调节器的两个任意子以及均匀磁场。这些描述散射或束缚态的格林函数（取决于每种情况下的特定势）是使用与SO（2，1）李群相关的代数方法精确获得的。从这些格林函数中我们得到了相应的波函数，对于束缚态，我们还得到了能谱。
英文摘要：
We calculate the Green's functions for the particle-vortex system, for two anyons on a plane with and without a harmonic regulator and in a uniform magnetic field. These Green's functions which describe scattering or bound states (depending on the specific potential in each case) are obtained exactly using an algebraic method related to the SO(2,1) Lie group. From these Green's functions we obtain the corresponding wave functions and for the bound states we also find the energy spectra.
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