Deriving new operator identities by alternately using normally,antinormally,and Weyl ordered integration technique  

作　　者：FAN HongYi1,YUAN HongChun1 & JIANG NianQuan2 1Department of Physics,Shanghai Jiao Tong University,Shanghai 200030,China 2College of Physics and Electric Information,Wenzhou University,Wenzhou 325035,China 

出　　处：《Science China(Physics,Mechanics & Astronomy)》2010年第9期1626-1630,共5页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos 10775097 and 10874174);the Special Funds of theNational Natural Science Foundation of China (Grant No 10947017/A05)

摘　　要：Dirac's ket-bra formalism is the language of quantum mechanics.We have reviewed how to apply Newton-Leibniz integration rules to Dirac's ket-bra projectors in previous work.In this work,by alternately using the technique of integration within normal,antinormal,and Weyl ordering of operators we not only derive some new operator ordering identities,but also deduce some new integration formulas regarding Laguerre and Hermite polynomials.This may open a new route of directly deriving some complicated mathematical integration formulas by virtue of the quantum mechanical operator ordering technique,without really performing the integrations in the ordinary way.Dirac’s ket-bra formalism is the language of quantum mechanics.We have reviewed how to apply Newton-Leibniz integration rules to Dirac’s ket-bra projectors in previous work.In this work,by alternately using the technique of integration within normal,antinormal,and Weyl ordering of operators we not only derive some new operator ordering identities,but also deduce some new integration formulas regarding Laguerre and Hermite polynomials.This may open a new route of directly deriving some complicated mathematical integration formulas by virtue of the quantum mechanical operator ordering technique,without really performing the integrations in the ordinary way.

关 键 词：OPERATOR ordering IDENTITIES LAGUERRE and HERMITE polynomials the IWOP technique 

分 类 号：O413.1[理学—理论物理]