论文标题
具有库仑电势的狄拉克方程的一般解
General solution of the Dirac equation with the Coulomb potential
论文作者
论文摘要
研究了带有库仑电势的狄拉克方程。结果表明，除了已知的迪拉克和约翰逊·莱克曼之外，还有一个新的不变。使用广义不变的狄拉克方程的解和对应于不变的三组，它们的特征值和量子数的双层的显式表达式。具有库仑电势的狄拉克方程的一般解决方案显示出包含游离参数，其变异将一种特定溶液转化为其他任何溶液，并控制空间电子概率幅度和自旋极化。电子概率密度和自旋极化以一般形式获得，并针对氢样能谱中某些电子状态明确计算。这些特征的空间分布显示出基本上取决于不变集，这表明了与不同不变的状态的物理差异。
The Dirac equation with the Coulomb potential is studied. It is shown that there exists a new invariant in addition to the known Dirac and Johnson-Lippman ones. The solution of the Dirac equation, using the generalized invariant, and explicit expressions for the bispinors corresponding to the three sets of the invariants, their eigenvalues and quantum numbers are obtained. The general solution of the Dirac equation with the Coulomb potential is shown to contain free parameters, whose variation transforms one particular solution into any other and controls spatial electron probability amplitude and spin polarization. The electron probability densities and spin polarizations are obtained in the general form and calculated explicitly for some electron states in the hydrogen-like energy spectrum. The spatial distributions of these characteristics are shown to depend essentially on the invariant set, demonstrating physical difference of the states corresponding to different invariants.
