Solution of Dirac Equation with Generalized Hylleraas Potential

We employ the parametric generalization of the Nikiforov-Uvarov method to solve the Alhaidari formalism of the Dirac equation with a generalized Hylleraas potential of the form V(r) = V0(a+exp(λr))/(b+ exp(λr)) + V1(d+exp(λr))/(b+exp(λr)).We obtain the bound state energy eigenvalue and the corresponding eigenfunction expressed in terms of the Jacobi polynomials.By choosing appropriate parameter in the potential model,the generalized Hylleraas potential reduces to the well known potentials as special cases.     

基于手性声子晶体的谷拓扑声输运

研究手性风车形散射体构建的谷拓扑声波导。具有右手与左手手性风车形散射体的声子晶体具有截然不同的声谷拓扑特性。当两种手性风车形散射体从-60°旋转到60°时,其所构建的声子晶体均出现2次偶然简并的狄拉克点与谷霍尔相变。基于两种具有相反谷霍尔相的手性声子晶体构建的谷拓扑声波导,在其重叠体带隙内存在一对局域在波导分界面处的谷态边缘态。实验研究表明,该边缘态可以很好的支持谷拓扑声输运,且对弯曲与无序两种缺陷具有一定的鲁棒性.     

有限空间中经典场的正则量子化

从离散的角度研究带边界的1+1维经典标量场和Dirac场的正则量子化问题. 与以往不同的是, 这里将时间和空间两个变量同时进行变步长的离散, 应用变步长离散的变分原理, 得到离散形式的运动方程、边界条件和能量守恒的表达式. 然后, 根据Dirac理论, 将边界条件当作初级约束, 将边界条件和内在约束统一处理. 研究表明, 采用此方法, 不仅在每个离散的时空格点上能够建立起Dirac括号, 从而可以完成该模型的正则量子化;而且, 该方法还保持了离散情况下的能量守恒.     

二维六角晶体材料中的Dirac 电子

本文综述由碳、硅、硼氮和二硫化钼等单元素或双元素构成的二维六角晶体材料中Dirac 电 子的研究成果与最新进展。文章从引言开始,接着介绍这些二维六角晶体材料的空间结构和基本 电子性质;然后探讨外场调控下这些材料在能谱和光吸收、量子输运、激子凝聚和热Josephson 效 应,以及拓扑量子相变等方面所表现出来的新奇的物理现象、简要的理论处理和可能的应用前景; 最后给出二维六角晶体材料相关研究的总结和展望。谨以本文献给南京大学建立物理学科100 周 年。     

Exact Solution to the One-Dimensional Dirac Equation with Time Varying Mass

We directly use the quantum-invariant operator method to obtain the closed-form solution to the one-dimensional Dirac equation with a time-changing mass with a little manipulation. The solution got is also applicable forthe case with time-independence mass.     

Spin and Pseudospin Symmetries of Dirac Equation and the Yukawa Potential as the Tensor Interaction

Considering of a tensor interaction in Dirac equation removes the degeneracy in spin and pseudospin doublets and consequently leads to results consistent with the experimental data. Here, instead of the commonly used Coulomb or linear terms, we investigate a tensor interaction of Yukawa form. We obtain arbitrary state solutions of Dirac equation under vector, scalar and tensor Yukawa potentials via a physical approximation and the Nikiforov-Uvarov methodology. The solutions are discussed in detail.