AI 中文总结
本文在狄拉克理论中求解带电原子链束缚电子的狄拉克方程，得到解析解，证明电子完全集体化，能量为占据数函数，并揭示谱带分裂为n个子带的精细结构。
AI 中文摘要
在狄拉克理论框架下研究了被带电原子链束缚的电子系统。得到了狄拉克方程的普遍解析解。推导出了电子能量的解析表达式，由此可知，在这样的系统中，电子态可以引入主量子数，类似于氢原子的情形。我们证明了被原子链束缚的电子是完全集体化的，并且能量可以表示为占据数的函数。主量子数为$n$的谱带被证明分裂为$n$个子带，形成精细结构。计算了精细结构分裂的尺度。
英文摘要
The system of electrons bound by a charged atom chain is studied within the Dirac theory. The general analytical solution of the Dirac equation is obtained. Analytical expression for electron energy is derived from which it follows that the principal quantum number can be introduced for electron states in such a system, similar to the case of a hydrogen atom. We prove that electrons bound by the atomic chain, are fully collectivized and the energy can be calculated as a function of the occupation number. The spectral band with the principal quantum number $n$ is shown to be split into $n$ subbands forming the fine structure. The scale of the fine structure splitting is calculated.
Comments17 pages
