New approach for normally ordering coordinate-operator functions

作者：Xu, Shi-min; Xu, Xing-lei; Li, Hong-qi^*; Fan, Hong-yi

来源：Optik, 2016, 127(20): 9961-9965.

DOI：10.1016/j.ijleo.2016.07.064

• Normal ordering
• Operator's differentiation
• IWOP technique

By virtue of the integration technique within ordered product of operators and Dirac's representation theory we find a new formula for normally ordering coordinate-operator functions, that is f((Q) over cap) =, exp (1/4 partial derivative(2)/partial derivative(Q) over cap)(2) f((Q) over cap) :, where (Q) over cap is the coordinate operator, the symbol :: denotes normal ordering. Using this formula we can arrange a given quantum operator function f((Q) over cap) in its normal ordering conveniently and fast. Furthermore, we can derive a series of new relations about Hermite polynomial and Laguerre polynomial, as well as some new differential relations. 0 2016 Published by Elsevier GmbH.

• 出版日期2016
• 单位中国科学技术大学; 菏泽学院