Simple approach to deriving operator identities and mathematical formulas regarding to two-variable Hermite polynomials |
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Authors: | Jun Zhou Jun SongHao Yuan |
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Affiliation: | Department of Material and Chemical Engineering, West Anhui University, Luan, Anhui 237012, China |
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Abstract: | By virtue of operator ordering technique and the generating function of polynomials, we provide a simple and neat approach to studying operator identities and mathematical formulas regarding to two-variable Hermite polynomials, which differs from the existing mathematical ways. We not only derive some new integration formulas and summation relations about two-variable Hermite polynomial, but also draw a conclusion that two-variable Hermite polynomial excitation of two-mode squeezed vacuum state is a squeezed two-mode number state. This may open a new route of developing mathematics by virtue of the quantum mechanical representations and operator ordering technique. |
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Keywords: | 03.65.&minus w 02.30.Cj |
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