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Chin. Phys. B, 2015, Vol. 24(10): 100302    DOI: 10.1088/1674-1056/24/10/100302
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A new kind of special function and its application

Fan Hong-Yi (范洪义)a, Wan Zhi-Long (万志龙)a, Wu Ze (吴泽)b, Zhang Peng-Fei (张鹏飞)b
a Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China;
b Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
Abstract  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.
Keywords:  new special function      new operator identities and integration formulas      Hermite-polynomial excitation state      integration within ordered product of operators (IWOP) method  
Received:  27 February 2015      Revised:  06 May 2015      Accepted manuscript online: 
PACS:  03.65.-w (Quantum mechanics)  
  42.50.-p (Quantum optics)  
  02.30.Gp (Special functions)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11175113).
Corresponding Authors:  Fan Hong-Yi     E-mail:  fhym@ustc.edu.cn

Cite this article: 

Fan Hong-Yi (范洪义), Wan Zhi-Long (万志龙), Wu Ze (吴泽), Zhang Peng-Fei (张鹏飞) A new kind of special function and its application 2015 Chin. Phys. B 24 100302

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