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A theorem for quantum operator correspondence to the solution of the Helmholtz equation |
| Fan Hong-Yi (范洪义)a, Chen Jun-Hua (陈俊华)b, Zhang Peng-Fei (张鹏飞)c, He Rui (何锐)d |
a Department of Physics, Ningbo University, Ningbo 315211, China;
b Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China;
c Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China;
d College of Material and Chemical Engineering, West Anhui University, Luan 237012, China |
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Abstract We propose a theorem for the quantum operator that corresponds to the solution of the Helmholtz equation, i.e.,∫∫∫V(x1,x2,x3|x1,x2,x3><x1,x2,x3|d3x = V(X1,X2,X3) = e-λ2/4:V(X1,X2,X3):,where IV(x1,x2,x3) is the solution to the Helmholtz equation ∇2V+λ2V=0, the symbol::denotes normal ordering, and X1,X2,X3 are three-dimensional coordinate operators. This helps to derive the normally ordered expansion of Dirac's radius operator functions. We also discuss the normally ordered expansion of Bessel operator functions.
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Received: 21 March 2014
Revised: 22 April 2014
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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02.30.Gp
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(Special functions)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11175113). |
Corresponding Authors:
Fan Hong-Yi, Chen Jun-Hua
E-mail: fhym@ustc.edu.cn;cjh@ustc.edu.cn
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Cite this article:
Fan Hong-Yi (范洪义), Chen Jun-Hua (陈俊华), Zhang Peng-Fei (张鹏飞), He Rui (何锐) A theorem for quantum operator correspondence to the solution of the Helmholtz equation 2014 Chin. Phys. B 23 110301
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