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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| Published in | Chinese physics B Vol. 25; no. 8; pp. 26 - 29 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
01.08.2016
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1674-1056 2058-3834 1741-4199 |
| DOI | 10.1088/1674-1056/25/8/080303 |
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| Abstract | 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. |
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| AbstractList | 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. 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. |
| Author | 陈锋 范洪义 |
| AuthorAffiliation | Department of Mathematics and Physics, Hefei University, Hefei 2306011 China Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China |
| Author_xml | – sequence: 1 fullname: 陈锋 范洪义 |
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| Cites_doi | 10.1016/j.aop.2005.09.011 10.1140/epjd/e2006-00278-8 10.1103/PhysRevA.49.704 10.1103/PhysRevA.77.042316 10.1103/PhysRevLett.101.080503 10.1142/S0217984907012943 |
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| Notes | 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 |
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| References | 11 1 12 2 Yangjian C (5) 2007; 24 Fan H Y (7) 2014; 23 4 Mazhar Ali (3) 2010; 43 9 Fan H Y (10) 2015; 24 Fan H Y (6) 2013; 22 Chen F (8) 2014; 23 |
| References_xml | – volume: 43 issn: 0953-4075 year: 2010 ident: 3 publication-title: J. Phys. B: At. Mol. Opt. Phys. – ident: 11 doi: 10.1016/j.aop.2005.09.011 – ident: 12 doi: 10.1140/epjd/e2006-00278-8 – volume: 23 issn: 1674-1056 year: 2014 ident: 7 publication-title: Chin. Phys. – volume: 24 issn: 1674-1056 year: 2015 ident: 10 publication-title: Chin. Phys. – ident: 9 doi: 10.1103/PhysRevA.49.704 – ident: 1 doi: 10.1103/PhysRevA.77.042316 – ident: 2 doi: 10.1103/PhysRevLett.101.080503 – volume: 23 issn: 1674-1056 year: 2014 ident: 8 publication-title: Chin. Phys. – ident: 4 doi: 10.1142/S0217984907012943 – volume: 24 start-page: 2394 issn: 0740-3232 year: 2007 ident: 5 publication-title: J. Opt. Soc. Am. – volume: 22 issn: 1674-1056 year: 2013 ident: 6 publication-title: Chin. Phys. |
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| Snippet | 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... |
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| SubjectTerms | 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 |
| Title | New useful special function in quantum optics theory |
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