Multi-variable special polynomials using an operator ordering method

Using an operator ordering method for some commutative superposition operators, we introduce two new multi-variable special polynomials and their generating functions, and present some new operator identities and integral formulas involving the two special polynomials. Instead of calculating complic...

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Bibliographic Details
Published in:Frontiers of physics 2020-10, Vol.15 (5), p.52501, Article 52501
Main Authors: Meng, Xiang-Guo, Li, Kai-Cai, Wang, Ji-Suo, Yang, Zhen-Shan, Zhang, Xiao-Yan, Zhang, Zhen-Tao, Liang, Bao-Long
Format: Article
Language:English
Subjects:
Astronomy
Astrophysics and Cosmology
Atomic
Condensed Matter Physics
Fourier transforms
Functions (mathematics)
generating function
Mathematical analysis
Molecular
multi-variable special polynomial
new operator identity and integral formula
operator ordering method
Operators (mathematics)
Optical and Plasma Physics
Partial differential equations
Particle and Nuclear Physics
Physics
Physics and Astronomy
Polynomials
Research Article
Wigner distribution
Wigner function
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Summary:Using an operator ordering method for some commutative superposition operators, we introduce two new multi-variable special polynomials and their generating functions, and present some new operator identities and integral formulas involving the two special polynomials. Instead of calculating complicated partial differential, we use the special polynomials and their generating functions to concisely address the normalization, photocount distributions and Wigner distributions of several quantum states that can be realized physically, the results of which provide real convenience for further investigating the properties and applications of these states.
ISSN:2095-0462
2095-0470
DOI:10.1007/s11467-020-0967-3