用于处理原子壳模型的代数工具。I.类氢离子的波函数和积分
Algebraic tools for dealing with the atomic shell model. I. Wavefunctions and integrals for hydrogen--like ions
摘要：
今天，众所周知，“氢原子模型”不仅在量子力学的基本原理教学中发挥作用，而且在原子和分子物理学、量子光学、等离子体物理甚至半导体器件的设计中建立有效的理论。因此，分析以及类氢离子的数值解经常需要，分析实验数据和进行相当先进的理论研究。为了支持一个快速和一致的访问这些（库仑场）的解决方案，在这里，我们提出了狄拉克程序，最初已开发的研究（类氢）离子的性质和动力学行为。在目前的版本中，一套Maple程序提供了库仑波和格林函数应用（波）方程从两个，非相对论和相对论理论。此外，除了交互式访问这些功能，一些径向积分也实现了狄拉克程序，这可能有助于用户构建跃迁振幅和截面，因为它们经常发生在离子-原子和离子-光子碰撞理论。
英文摘要：
Today, the 'hydrogen atom model' is known to play its role not only in teaching the basic elements of quantum mechanics but also for building up effective theories in atomic and molecular physics, quantum optics, plasma physics, or even in the design of semiconductor devices. Therefore, the analytical as well as numerical solutions of the hydrogen--like ions are frequently required both, for analyzing experimental data and for carrying out quite advanced theoretical studies. In order to support a fast and consistent access to these (Coulomb--field) solutions, here we present the Dirac program which has been developed originally for studying the properties and dynamical behaviour of the (hydrogen--like) ions. In the present version, a set of Maple procedures is provided for the Coulomb wave and Green's functions by applying the (wave) equations from both, the nonrelativistic and relativistic theory. Apart from the interactive access to these functions, moreover, a number of radial integrals are also implemented in the Dirac program which may help the user to construct transition amplitudes and cross sections as they occur frequently in the theory of ion--atom and ion--photon collisions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
