New approach for normally ordering coordinate-operator functions

Shi-Min Xu, Xing-Lei Xu, Hongqi Li +1 more

Lei Wang, Xiang‐Guo Meng, Ji‐Suo Wang

By using the parameter differential method of operators, we recast the combination function of coordinate and momentum operators into its normal and anti-normal orderings, which is more ecumenical, simpler, and neater than the existing ways. These products are very useful in obtaining some new differential relations and useful mathematical integral formulas. Further, we derive the normally ordered form of the operator (fQ + gP)−n with n being an arbitrary positive integer by using the parameter tracing method of operators together with the intermediate coordinate–momentum representation. In addition, general mutual transformation rules of the normal and anti-normal orderings, which have good universality, are derived and hence the anti-normal ordering of (fQ + gP)−n is also obtained. Finally, the application of some new identities is given.

YU Zhi-son

In this paper,we introduce a new nonclassical quantum state,an inverse coordinate operator excited coherent state.By using the IWOP technique,the normally ordering form of inverse coordinate operator and the normalization factor are derived.It is shown that the normally ordering form is related to Hermit polynomial.On the basis of the coherent state representation of the Wigner operator,the Wigner function is also calculated,whose negative property is used to discuss the nonclassical property of the nonclassical quantum state.

L. F. Blazhievskii

Hong-Yi Fan, Hong‐Chun Yuan, Gen-Chang Cai +1 more

Shao Yu-Chong, Fan Hong-Yi

For Hermite polynomials of radial coordinate operator in three-dimensional coordinate space we derive its normal ordering expansion, which are new operator identities. This is done by virtue of the technique of integration within an ordered product of operators. Application of the new formulas is briefly discussed.