›› 2014, Vol. 23 ›› Issue (11): 110301-110301.doi: 10.1088/1674-1056/23/11/110301

• GENERAL • 上一篇    下一篇

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

范洪义a, 陈俊华b, 张鹏飞c, 何锐d   

  1. 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
  • 收稿日期:2014-03-21 修回日期:2014-04-22 出版日期:2014-11-15 发布日期:2014-11-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 11175113).

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   

  1. 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
  • Received:2014-03-21 Revised:2014-04-22 Online:2014-11-15 Published:2014-11-15
  • Contact: Fan Hong-Yi, Chen Jun-Hua E-mail:fhym@ustc.edu.cn;cjh@ustc.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 11175113).

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摘要： 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.

关键词: normally ordered expansion, radius operators, Helmholtz equation, Bessel operator function

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.

Key words: normally ordered expansion, radius operators, Helmholtz equation, Bessel operator function

中图分类号:  (Quantum mechanics)

  • 03.65.-w
02.30.Gp (Special functions)