New useful special function in quantum optics theory

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.,min（m,n）∑l=0^min（m,n）n!m!（-1）^l/l!（n-1）!（m-l）!/Hn-...

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Bibliographic Details
Published inChinese physics B Vol. 25; no. 8; pp. 26 - 29
Main Author 陈锋 范洪义
Format Journal Article
LanguageEnglish
Published 01.08.2016
Subjects
Chin
Functions (mathematics)
Hermite polynomials
Hermite多项式
Mathematical analysis
Operators
Quantum optics
光学理论
操作者
正规乘积
特殊函数
生成函数
级数和
量子
Online AccessGet full text
ISSN1674-1056
2058-3834
1741-4199
DOI10.1088/1674-1056/25/8/080303

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Summary: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.,min（m,n）∑l=0^min（m,n）n!m!（-1）^l/l!（n-1）!（m-l）!/Hn-l（x）y^m-l≡ n,m（x,y）.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.
Bibliography:Hermite polynomial excitation state, IWOP method, new special function, generating function,operator Hermite polynomial method
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.,min（m,n）∑l=0^min（m,n）n!m!（-1）^l/l!（n-1）!（m-l）!/Hn-l（x）y^m-l≡ n,m（x,y）.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.
Feng Chen,Hong-Yi Fan（1 Department of Mathematics and Physics, Hefei University, Hefei 2306011 China ;2Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China）
11-5639/O4
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1674-1056
2058-3834
1741-4199
DOI:10.1088/1674-1056/25/8/080303