计算机代数在量子力学和量子电动力学中的应用

ON APPLICATION OF COMPUTER ALGEBRA IN QUANTUM M ECHANICS AND QUANTUM ELECTRODYNAMICS

本文通过作者具体工作的几个例子说明计算机代数在量子力学和量子电动力学中的应用。它们是:①以一维多项式幂次势的计算为例说明升降算符的计算机代数处理方法;②以因式分解法解三维谐振子径向方程为例说明解析递推关系和公式匹配的计算机处理;③以特殊函数为例说明递归的使用方法;④以Compton散射和电子-电子散射为例说明γ矩阵和Feynman图的计算机代数处理方法。并且最后讨论了在量子力学和量子电动力学中应用计算机代数的一些情况。

Several examples worked out by the author are given to illustrate the applications of computer algebra (CA) in Quantum Mechanics and Quantum Electrodynamics. They are:1) reduce approach to one- dimension polynomial anharmonic oscillator to show the treatmenpt for uand down ladder operators in CA;2)The factorization method for three-dimensional oscillator to show the method for formula match and re-currence relation in CA;3) The analytical derivation of special functions to show the recursion method in GA; 4) The Compton scatter and electron - electron scatter to show the calculation of Gamma matrix and Feynmam diagram. In the end of this paper a simple survey o f the applications of computer algebra in these two fields is given.