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

作　　者：王党朝 陈湘[1] 王剑[1] 黄永超[1] WANG Dangchao;CHEN Xiang;WANG Jian;HUANG Yongchao(School of Physics and Electronic Information Engineering,Neijiang Normal University,Neijiang 641100,Sichuan,China)

机构地区：[1]内江师范学院物理与电子信息工程学院,四川内江641100

出　　处：《咸阳师范学院学报》2023年第4期15-17,共3页Journal of Xianyang Normal University

基　　金：内江师范学院引进人才项目(00018B05)。

摘　　要：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.

关 键 词：傅里叶变换 奇点 留数定理 围道积分 

分 类 号：O411.1[理学—理论物理]