对一类定积分问题使用留数定理求解的探讨

A Further Discussion of a Category of Integral Problem Using the Residue Theorem

针对量子力学和固体物理学中一类无法求解出原函数的实变定积分问题,先使用幂级数理论求解,再使用复变函数理论中的留数定理求解,两种方法结果一致。结果表明,通过构造积分围道,使用复变函数中留数定理求解的方法可以有效解决该类定积分问题。

Taking a class of real-variable function definite integral that cannot be solved in the in quantum mechanics and solid state physics as an example,the power series theory is first used,and then solved by the residue theorem in the theory of complex variable functions,and the results are the same.The results show that such definite integration problems can be solved by constructing an integral contour and using the residue theorem in the complex function.It is hoped that our research results will enrich the field of solving definite integral problems of real-variable function using complex variable function theory.