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New useful special function in quantum optics theory |
| Feng Chen(陈锋)1, Hong-Yi Fan(范洪义)2 |
1 Department of Mathematics and Physics, Hefei University, Hefei 230601, China;
2 Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China |
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Abstract By virtue of the operator Hermite polynomial method[Fan H Y and Zhan D H 2014Chin. Phys. B 23 060301] we find a new special function which is useful in quantum optics theory, whose expansion involving both power-series and Hermite polynomials, i.e.,
.jpg) (n!m!(-1)l/l!(n-l)!(m-l)!)Hn-l(x)ym-l≡ϑn, 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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Received: 16 February 2016
Revised: 06 April 2016
Accepted manuscript online:
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PACS:
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03.65.-w
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(Quantum mechanics)
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42.50.-p
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(Quantum optics)
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| Fund: Project supported by the Natural Science Fund of Education Department of Anhui Province, China (Grant No. KJ2016A590), the Talent Foundation of Hefei University, China (Grant No. 15RC11), and the National Natural Science Foundation of China (Grant Nos. 11247009 and 11574295). |
Corresponding Authors:
Feng Chen
E-mail: chenfeng@hfuu.edu.cn
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Cite this article:
Feng Chen(陈锋), Hong-Yi Fan(范洪义) New useful special function in quantum optics theory 2016 Chin. Phys. B 25 080303
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