A theorem for quantum operator correspondence to the solution of the Helmholtz equation

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 V （X1 ,X2,X3） is the solution to the Helmholtz equation △2V ＋λ2V = 0, the symbol ： ： denotes normal...

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Published inChinese physics B Vol. 23; no. 11; pp. 157 - 160
Main Author 范洪义 陈俊华 张鹏飞 何锐
Format Journal Article
LanguageEnglish
Published 01.11.2014
Subjects
Helmholtz equations
Operators
Order disorder
Symbols
Theorems
Three dimensional
三维坐标
亥姆霍兹方程
定理
操作功能
狄拉克
运算符
通信运营商
量子
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Summary: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 V （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.
Bibliography: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 V （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.
Fan Hong-Yi, Chen Jun-Hua, Zhang Peng-Fei, and He Rui（ 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 Modem Physics, University of Science and Technology of China, Hefei 230026, China d） College of Material and Chemical Engineering, West Anhui University, Luan 237012, China
11-5639/O4
normally ordered expansion, radius operators, Helmholtz equation, Bessel operator function
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1674-1056
2058-3834
1741-4199
DOI:10.1088/1674-1056/23/11/110301