具有一维Coulomb型对称势Dirac方程的精确解

Exact solutions for Dirac equation with one dimensional symmetric Coulomb type potentials

在标量势大于矢量势的情况下 ,一维Dirac方程的束缚态能级是二重简并的 .任意两个不同能量本征值的波函数和同一能量本征值的两个波函数都是相互正交的 .对于纯标量场 ,存在零能量束缚态 。

The energy levels of bound states for one dimensional Dirac equation are doubly degenerate provided that the scalar like potential is greater than the vector like potential. Arbitrary two wave functions with different eigenenergies and two wave functions with the same eigenenergy are orthogonal to each other. For a pure scalar potential the zero energy bound state does exist, and the fractional charge does exist.