Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Theoretical Physics

New General Approach for Normally Ordering Coordinate-Momentum Operator Functions

Shi-Min Xu, Xing-Lei Xu, Hongqi Li, Hong-Yi Fan

Published Sep 13, 2016• 0 citations
Publisher
DOI
10.1007/s10773-016-3155-z

Related papers

New approach for normally ordering coordinate-operator functions

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

Optik•Jul 29, 2016•0 citations

New fundamental quantum mechanical operator-ordering identities for the coordinate and momentum operators

Hong-Yi Fan

Science China Physics Mechanics and Astronomy•Mar 25, 2012•19 citations

Recast combination functions of coordinate and momentum operators into their ordered product forms*

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.

Chinese Physics B•Mar 9, 2020•3 citations

Normally ordered expansion of the inverse of the coordinate operator and the momentum operator

Hong-Yi Fan, Liang Fu

We derive the normally ordered expansion formulae of 1/ n and 1/ n by virtue of the method of integral within an ordered product of operators in the sense of the principal value integral, where , are the coordinate and momentum operator, respectively. Application of the new formula is briefly discussed.

Journal of Physics A Mathematical and General•Apr 24, 2003•15 citations

Derivation of wave functions of particle number state by using Hermite polynomial operator

Fan Hong-Yi

By introducing the Hermite polynomial operator and deriving its normally ordered expansion,we derive the wave functions of particle number state in the coordinate representation and momentum representation,respectively,which can directly lead to the Fock representation of coordinate and momentum eigenstate.Our way is brand-new and concise.

College Physics•Jan 1, 2011•0 citations

Equivalence of Momentum Operators in Generalized Coordinates

Gary R. Gruber

American Journal of Physics•Nov 1, 1972•3 citations
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.