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We propose an operator Hermite polynomial method, namely, to replace the special functions' argument by quantum mechanical operator, and in this way we have derived two binomial theorems related to two-variable Hermite polynomials. This method is concise and may be of help in deducing many operator identities, which may become a new branch in mathematical physics theory.
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Keywords:
- operator Hermite polynomial method /
- two-variable Hermite polynomials /
- operator identities
[1] Fan H Y, Lou S Y, Pan X Y, Da C 2013 Acta Phys. Sin. 62 240301 (in Chinese) [范洪义, 楼森岳, 潘孝胤, 笪诚 2013 62 240301]
[2] Fan H Y, Zhou J 2012 Science China, Physics, Mechanics m& Astronomy 55 605
[3] A. Erdelyi 1953 Higher Transcendental Functions (The Bateman Manuscript Project) (McGraw Hill)
[4] Fan H Y, Jiang T F 2007 Mod. phys. Lett. B 21 475
[5] Fan H Y, Tang X B 2008 Devolopment of basis of the mathematical physics of quantum mechanics (Hefei:USTC Press)(in Chinese) [范洪义, 唐绪兵 2008 量子力学数理基础进展(合肥: 中国科学技术大学出版社)]
[6] Fan H Y, Zhan D H, Yu W J, Zhou J 2012 Acta Phys. Sin. 61 110302 (in Chinese) [范洪义, 展德会, 于文健, 周军 2012 61 110302]
[7] Fan H Y, Lu H L, Fan Y 2006 Ann. Phys. 321 480
[8] Einstein A, Podolsky B, Rosen N 1935 Phys. Rev. 47 777
[9] Braunstein S L, Loock P V 2005 Rev. Mod. Phys. 77 513
[10] Fan H Y, Klauder J R 1994 Phys. Rev. A 49 704
[11] Fan H Y, Zaidi H R, Klauder J R 1987 Phys. Rev. D 35 1831
[12] Fan H Y 2003 J. Opt. B: Quantum Semiclass. Opt. 5 R147
[13] Liang X T, Fan H Y 2001 Chin. Phys. B 10 486 (in Chinese) [梁先庭, 范洪义 2001 中国物理 10 486]
[14] Fan H Y, Da C 2013 Chin. Phys. B 22 090303
[15] Arrechi F T, Courtons E, Gilmore R, Thomas H 1972 Phys. Rev. A 6 2211
[16] Schwinger J 1965 Quantum Theory of Angular momentum (New York:Academic press)
[17] Fan H Y, Chen J H 2003 Eur. Phys. J. D 23 437
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[1] Fan H Y, Lou S Y, Pan X Y, Da C 2013 Acta Phys. Sin. 62 240301 (in Chinese) [范洪义, 楼森岳, 潘孝胤, 笪诚 2013 62 240301]
[2] Fan H Y, Zhou J 2012 Science China, Physics, Mechanics m& Astronomy 55 605
[3] A. Erdelyi 1953 Higher Transcendental Functions (The Bateman Manuscript Project) (McGraw Hill)
[4] Fan H Y, Jiang T F 2007 Mod. phys. Lett. B 21 475
[5] Fan H Y, Tang X B 2008 Devolopment of basis of the mathematical physics of quantum mechanics (Hefei:USTC Press)(in Chinese) [范洪义, 唐绪兵 2008 量子力学数理基础进展(合肥: 中国科学技术大学出版社)]
[6] Fan H Y, Zhan D H, Yu W J, Zhou J 2012 Acta Phys. Sin. 61 110302 (in Chinese) [范洪义, 展德会, 于文健, 周军 2012 61 110302]
[7] Fan H Y, Lu H L, Fan Y 2006 Ann. Phys. 321 480
[8] Einstein A, Podolsky B, Rosen N 1935 Phys. Rev. 47 777
[9] Braunstein S L, Loock P V 2005 Rev. Mod. Phys. 77 513
[10] Fan H Y, Klauder J R 1994 Phys. Rev. A 49 704
[11] Fan H Y, Zaidi H R, Klauder J R 1987 Phys. Rev. D 35 1831
[12] Fan H Y 2003 J. Opt. B: Quantum Semiclass. Opt. 5 R147
[13] Liang X T, Fan H Y 2001 Chin. Phys. B 10 486 (in Chinese) [梁先庭, 范洪义 2001 中国物理 10 486]
[14] Fan H Y, Da C 2013 Chin. Phys. B 22 090303
[15] Arrechi F T, Courtons E, Gilmore R, Thomas H 1972 Phys. Rev. A 6 2211
[16] Schwinger J 1965 Quantum Theory of Angular momentum (New York:Academic press)
[17] Fan H Y, Chen J H 2003 Eur. Phys. J. D 23 437
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