广义Bessel函数阵列的递归算法：Dirac-Volkov解的数值逼近
Recursive algorithm for arrays of generalized Bessel functions: Numerical access to Dirac-Volkov solutions
摘要：
在中强激光与物质相互作用的相对论和非相对论理论处理中，当薛定谔-沃尔科夫和狄拉克-沃尔科夫解展开为平面波时，广义贝塞尔函数自然出现。为了计算线偏振激光场中量子电动力学过程的截面，常常需要计算任意指数但具有固定自变量的广义贝塞尔函数的大阵列。我们表明，广义贝塞尔函数可以评估，在一个数值稳定的方式，仅利用递归关系和归一化条件，而不必计算任何初始值。我们证明了该方法的实用性，说明量子经典对应的Dirac-Volkov解决方案，通过数值计算。
英文摘要：
In the relativistic and the nonrelativistic theoretical treatment of moderate and high-power laser-matter interaction, the generalized Bessel function occurs naturally when a Schrödinger-Volkov and Dirac-Volkov solution is expanded into plane waves. For the evaluation of cross sections of quantum electrodynamic processes in a linearly polarized laser field, it is often necessary to evaluate large arrays of generalized Bessel functions, of arbitrary index but with fixed arguments. We show that the generalized Bessel function can be evaluated, in a numerically stable way, by utilizing a recurrence relation and a normalization condition only, without having to compute any initial value. We demonstrate the utility of the method by illustrating the quantum-classical correspondence of the Dirac-Volkov solutions via numerical calculations.
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