论文标题
具有无限质量边界条件的Dirac-Coulomb操作员
Dirac-Coulomb Operators with Infinite Mass Boundary Conditions in Sectors
论文作者
论文摘要
我们研究了二维狄拉克操作员在具有无限质量边界条件的无限扇区上的自相关性的性质，并且在存在库仑型电势的情况下，将奇异性放在顶点上。在一般情况下，我们证明了适当的野性不平等现象并利用了加藤 - 瑞典理论。在库仑电势的明确情况下，我们描述了依赖于适应于无限质量边界条件的部分波浪子空间中径向分解的所有电势强度的自相关扩展。最后，我们整合了结果，以描述这些操作员的频谱。
We investigate the properties of self-adjointness of a two-dimensional Dirac operator on an infinite sector with infinite mass boundary conditions and in presence of a Coulomb-type potential with the singularity placed on the vertex. In the general case, we prove the appropriate Dirac-Hardy inequality and exploit the Kato-Rellich theory. In the explicit case of a Coulomb potential, we describe the self-adjoint extensions for all the intensities of the potential relying on a radial decomposition in partial wave subspaces adapted to the infinite-mass boundary conditions. Finally, we integrate our results giving a description of the spectrum of these operators.
