关于相对论性两点格林函数
On the relativistic two-point Green's function
摘要：
利用最近发展起来的求解三维球对称Dirac方程的方法，我们得到了Dirac振子和Dirac库仑问题的格林函数的简单表示.这是通过这样一种方式来实现的：相对论性问题的设置使得与非相对论性问题的比较高度透明，并导致后者到前者的映射。这种表示的优点在于计算经济性，如由项的数量所描绘的，其在惠特克函数中是二次的。这些都是单一的条款，除了非对角元素的狄拉克-库仑格林函数，但简化为一阶和三阶相对论性条款的总和。
英文摘要：
Using a recently developed approach for solving the three dimensional Dirac equation with spherical symmetry, we obtain simple representations for the Green's function of the Dirac-Oscillator and Dirac-Coulomb problems. This is accomplished by setting up the relativistic problem in such a way that makes comparison with the nonrelativistic problem highly transparent and results in a map of the latter into the former. An advantage of this representation is in the computational economy as depicted by the number of terms, which are quadratic in the Whittaker functions. These are single terms except for the off-diagonal elements of the Dirac-Coulomb Green's function which, nonetheless, simplifies into the sum of a first order and third order relativistic terms.
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