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

中国物理B：英文版

Generating function of product of bivariate Hermite polynomials and their applications in studying quantum optical states

范洪义, 张鹏飞, 王震

Published Jan 1, 2015• 1 citation
OpenAlex

Abstract

By virtue of the operator-Hermite-polynomial method, we derive some new generating function formulas of the product of two bivariate Hermite polynomials. Their applications in studying quantum optical states are presented.

Related papers

Generating function of product of bivariate Hermite polynomials and their applications in studying quantum optical states

Hong-Yi Fan, Pengfei Zhang, Zhen Wang

By virtue of the operator-Hermite-polynomial method, we derive some new generating function formulas of the product of two bivariate Hermite polynomials. Their applications in studying quantum optical states are presented.

Chinese Physics B•Apr 30, 2015•6 citations

Some new generating function formulae of the two-variable Hermite polynomials and their application in quantum optics

De-Hui Zhan, Hong-Yi Fan

We derive some new generating function formulae of the two-variable Hermite polynomials, such as H n ,2 m ( x ), H 2 n ,2 m ( x , y ), and H 2 n + l ,2 m + k ( x , y ). We employ the operator Hermite polynomial method and the technique of integration within an ordered product of operators to solve these problems, which will be useful in constructing new optical field states.

Chinese Physics B•Nov 28, 2014•2 citations

New generating function formulae of even- and odd-Hermite polynomials obtained and applied in the context of quantum optics

Hong-Yi Fan, De-Hui Zhan

By combining the operator Hermite polynomial method and the technique of integration within an ordered product of operators, for the first time we derive the generating function of even- and odd-Hermite polynomials which will be useful in constructing new optical field states. We then show that the squeezed state and photon-added squeezed state can be expressed by even- and odd-Hermite polynomials.

Chinese Physics B•May 30, 2014•8 citations

New useful special function in quantum optics theory

Feng Chen, Hong-Yi Fan

By virtue of the operator Hermite polynomial method [Fan H Y and Zhan D H 2014 Chin. Phys. B 23 060301] we find a new special function which is useful in quantum optics theory, whose expansion involves both power-series and Hermite polynomials, i.e., By virtue of the operator Hermite polynomial method and the technique of integration within ordered product of operators (IWOP) we derive its generating function. The circumstance in which this new special function appears and is applicable is considered.

Chinese Physics B•Jul 26, 2016•3 citations

New generating function formulae of even- and odd-Hermite polynomials obtained and applied in the context of quantum optics

范洪义, 展德会

By combining the operator Hermite polynomial method and the technique of integration within an ordered product of operators, for the first time we derive the generating function of even- and odd-Hermite polynomials which will be useful in constructing new optical field states. We then show that the squeezed state and photon-added squeezed state can be expressed by even- and odd-Hermite polynomials.

中国物理B：英文版•Jan 1, 2014•2 citations

A new kind of special function and its application

范洪义, M LONG, 吴泽 +1 more

By virtue of the operator Hermite polynomial method and the technique of integration within the ordered product of operators we derive a new kind of special function, which is closely related to one- and two-variable Hermite polynomials.Its application in deriving the normalization for some quantum optical states is presented.

中国物理B：英文版•Jan 1, 2015•0 citations
By virtue of the operator Hermite polynomial method [Fan H Y and Zhan D H 2014 Chin. Phys. B 23 060301] we find a new special function which is useful in quantum optics theory, whose expansion involves both power-series and Hermite polynomials, i.e., By virtue of the operator Hermite polynomial method and the technique of integration within ordered product of operators (IWOP) we derive its generating function. The circumstance in which this new special function appears and is applicable is considered.