屏蔽库仑势径向Klein-Gordon方程的$\hbar$展开式对数微扰理论
Logarithmic perturbation theory for radial Klein-Gordon equation with screened Coulomb potentials via $\hbar$ expansions
摘要：
在径向Klein-Gordon方程的框架内，利用对数微扰理论对束缚态问题进行了显式半经典处理，该方程具有吸引力的实解析屏蔽库仑势，包含Lorentz四矢量的时间分量和Lorentz标量项。基于$\hbar$ -展开式和适当的量子化条件，给出了一种推导微扰展开式的新方法.避免了标准方法的缺点，得到了基态和激发态具有相同简单形式的新的简便递推公式。作为一个例子，考虑了包含矢量部分和标量部分的Hulthén势的能量本征值的微扰展开.
英文摘要：
The explicit semiclassical treatment of logarithmic perturbation theory for the bound-state problem within the framework of the radial Klein-Gordon equation with attractive real-analytic screened Coulomb potentials, contained time-component of a Lorentz four-vector and a Lorentz-scalar term, is developed. Based upon $\hbar$-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both for ground and excited states have been obtained. As an example, the perturbation expansions for the energy eigenvalues for the Hulthén potential containing the vector part as well as the scalar component are considered.
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