Guvendi Abdullah, Sahin Ramazan, Sucu Yusuf
Akdeniz University Faculty of Science, Department of Physics, Antalya, 07058, Turkey.
Akdeniz University Vocational School of Technical Sciences, Antalya, 07058, Turkey.
Sci Rep. 2019 Jun 20;9(1):8960. doi: 10.1038/s41598-019-45478-4.
We present exact solutions of an energy spectrum of 2-interacting particles in which they seem to be relativistic fermions in 2 + 1 space-time dimensions. The 2 × 2 spinor equations of 2-interacting fermions through general central potential were separated covariantly into the relative and center of mass coordinates. First of all, the coupled first order differential equations depending on radial coordinate were derived from 2 × 2 spinor equations. Then, a second order radial differential equation was obtained and solved for Coulomb interaction potential. We apply our solutions to exciton phenomena for a free-standing monolayer medium. Since we regard exciton as isolated 2-interacting fermions in our model, any other external effect such as substrate was eliminated. Our results show that the obtained binding energies in our model are in agreement with the literature. Moreover, the decay time of an exciton was found out spontaneously in our calculations.
我们给出了两个相互作用粒子的能谱的精确解，其中它们在2 + 1时空维度中似乎是相对论费米子。通过一般中心势的两个相互作用费米子的2×2旋量方程被协变分离为相对坐标和质心坐标。首先，从2×2旋量方程导出了依赖于径向坐标的耦合一阶微分方程。然后，得到了一个二阶径向微分方程并求解了库仑相互作用势。我们将我们的解应用于独立单层介质的激子现象。由于在我们的模型中我们将激子视为孤立的两个相互作用费米子，所以消除了任何其他外部效应，如衬底。我们的结果表明，我们模型中得到的结合能与文献一致。此外，在我们的计算中自发地发现了激子的衰变时间。
