二维带电荷和磁通量粒子的量子力学模型
Quantum-mechanical model for particles carrying electric charge and magnetic flux in two dimensions
摘要：
我们提出了一个简单的量子力学方程的$n$粒子在二维，每个粒子携带电荷和磁通量。这样的粒子出现在（2+1）维陈-西蒙斯场理论中作为带电涡旋孤子解，其中电荷与通量之比是一个常数，与具体的解决方案无关。作为近似，电荷-通量相互作用在这里由Aharonov-Bohm势描述，电荷-电荷相互作用由库仑势描述。详细研究了两个粒子的方程，一个粒子带有电荷和通量（$q, Φ/Z$），另一个粒子带有电荷和通量（$-Zq, -Φ$），其中$Z$是纯数.当$q$.当$qΦ/2π\hbar c$取整数或半整数时，在抛物坐标系下精确求解了散射问题.在这两种情况下得到的横截面是相当不同的纯库仑散射。
英文摘要：
We propose a simple quantum mechanical equation for $n$ particles in two dimensions, each particle carrying electric charge and magnetic flux. Such particles appear in (2+1)-dimensional Chern-Simons field theories as charged vortex soliton solutions, where the ratio of charge to flux is a constant independent of the specific solution. As an approximation, the charge-flux interaction is described here by the Aharonov-Bohm potential, and the charge-charge interaction by the Coulomb one. The equation for two particles, one with charge and flux ($q, Φ/Z$) and the other with ($-Zq, -Φ$) where $Z$ is a pure number is studied in detail. The bound state problem is solved exactly for arbitrary $q$ and $Φ$ when $Z>0$. The scattering problem is exactly solved in parabolic coordinates in special cases when $qΦ/2π\hbar c$ takes integers or half integers. In both cases the cross sections obtained are rather different from that for pure Coulomb scattering.
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