Quantum mechanical operator realization of the Stirling numbers theory studied by virtue of the operator Hermite polynomials method

doi:10.1088/1674-1056/24/7/070305

Abstract Based on the operator Hermite polynomials method (OHPM), we study Stirling numbers in the context of quantum mechanics, i.e., we present operator realization of generating function formulas of Stirling numbers with some applications. As a by-product, we derive a summation formula involving both Stirling number and Hermite polynomials.

Keywords: operator Hermite polynomials method (OHPM) Stirling numbers

Received: 10 January 2015
Revised: 05 February 2015
Accepted manuscript online:

PACS:	03.65.-w	(Quantum mechanics)
	42.50.-p	(Quantum optics)

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

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Fan Hong-Yi (范洪义), Lou Sen-Yue (楼森岳) Quantum mechanical operator realization of the Stirling numbers theory studied by virtue of the operator Hermite polynomials method 2015 Chin. Phys. B 24 070305

[1]	Abramowitz M and Stegun I 1972 Stirling Numbers of the First Kind, in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (New York: Dover) p. 824
[2]	Fan H Y, Ou-Yang J and Jiang Z H 2006 Commun. Theor. Phys. 45 49
[3]	Fan H Y and Jiang N Q 2010 Commun. Theor. Phys. 54 651
[4]	Fan H Y and Zhou J 2012 Sci. China: Phys. Mech. Astron. 55 605
[5]	Fan H Y and Zhan D H 2014 Chin. Phys. B 23 060301
[6]	Fan H Y, Zhang P F and Wang Z 2014 Chin. Phys. B
[7]	Lu H L and Fan H Y 2007 Commun. Theor. Phys. 47 1024
[8]	Fan H Y and Fan Y 2000 Commun. Theor. Phys. 34 149
[9]	Fan H Y 2004 Commun. Theor. Phys. 42 339
[10]	Fan H Y, Lou S Y, Pan X Y and Da C 2013 Acta Phys. Sin. 62 240301 (in Chinese)
[11]	Fan H Y, Lou S Y, Pan X Y and Da C 2014 Acta Phys. Sin. 63 110304 (in Chinese)
[12]	Fan H Y, Lu H L and Fan Y 2006 Ann. Phys. 321 480

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Quantum mechanical operator realization of the Stirling numbers theory studied by virtue of the operator Hermite polynomials method

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