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

Chinese Physics B

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

De-Hui Zhan, Hong-Yi Fan

Published Nov 28, 2014• 2 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/23/12/120301

Related papers

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

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 approach to generating functions of single- and two-variable even- and odd-Hermite polynomials and applications in quantum optics

Fang Jia, Shuang Xu, Liyun Hu +2 more

Using the IWOP technique and completeness of representation, we obtain the integral expressions of single- and two-variable Hermite polynomials. Based on this, we further derive the generating functions of single- and two-variable even- and odd-Hermit polynomials. This method seems more concise and direct. In addition, some applications such as deriving new formula and constructing new two-mode quantum states are discussed. It is found that two-variable Hermite polynomials excitation can used to produce entangled coherent states.

Modern Physics Letters B•Dec 30, 2014•4 citations

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

范洪义, 张鹏飞, 王震

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.

中国物理B：英文版•Jan 1, 2015•1 citation

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

Entangled state representation for deriving new operator identities regarding to two-variable Hermite polynomial

Hong-Yi Fan, Hong-chun Yuan

In this paper, by virtue of the entangled state representation we concisely derive some new operator identities regarding to two-variable Hermite polynomial (TVHP). By them and the technique of integration within an ordered product (IWOP) of operators we further derive new generating function formulas of TVHP. They are useful in quantum optical theoretical calculations. It is seen from this work that by combining the IWOP technique and quantum mechanical representations one can derive some new integration formulas even without really performing the integration.

arXiv:1011.5943•Nov 27, 2010•0 citations
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.
Using the IWOP technique and completeness of representation, we obtain the integral expressions of single- and two-variable Hermite polynomials. Based on this, we further derive the generating functions of single- and two-variable even- and odd-Hermit polynomials. This method seems more concise and direct. In addition, some applications such as deriving new formula and constructing new two-mode quantum states are discussed. It is found that two-variable Hermite polynomials excitation can used to produce entangled coherent states.
In this paper, by virtue of the entangled state representation we concisely derive some new operator identities regarding to two-variable Hermite polynomial (TVHP). By them and the technique of integration within an ordered product (IWOP) of operators we further derive new generating function formulas of TVHP. They are useful in quantum optical theoretical calculations. It is seen from this work that by combining the IWOP technique and quantum mechanical representations one can derive some new integration formulas even without really performing the integration.