多算符连乘式对易关系展开结果的普适公式  

Universal formula for the expansion of the commutation relation of multi-operators multiplication

作　　者：王乾行 李鹏 WANG Qian-xing;LI Peng(School of Physics and Electronics,Henan University,Kaifeng,Henan 475004,China;National Demonstration Center for Experimental Physics and Electronics Education,Henan University,Kaifeng,Henen 475004,China)

机构地区：[1]河南大学物理与电子学院,河南开封475004 [2]河南大学国家级物理与电子实验教学示范中心,河南开封475004

出　　处：《大学物理》2020年第10期81-85,共5页College Physics

基　　金：河南大学物理与电子学院首批核心课程《量子力学》建设项目(02301107);河南大学2018年度本科教学改革项目(HDXJJG2018-115)。

摘　　要：本文中对多算符乘积的对易关系展开结果进行了研究,发现了一个普适展开公式,并对该公式进行了严格证明.利用该公式可以直接给出多算符乘积的对易关系式展开结果.采用该公式对一些常见量子力学算符对易关系进行展开,展开后的结果与通过正常程序展开的结果相同,这也进一步印证了该公式的正确性.The expansion results of the commutation relation of multi-operators multiplication are studied,and a universal expansion formula is found.The formula can be proved strictly,and the proof process is also shown.The formula can directly show the expansion result of the commutation relation for multi-operators multiplication.The formula is used to expand the commutation relation of some common quantum mechanics operators.The expanded results using the formula are the same as that obtained through the normal procedure.These results further confirm the correctness of the formula.

关 键 词：对易关系 多算符乘积 普适公式 数学归纳法 

分 类 号：O413.1[理学—理论物理]