Cite this article:
Fan Hong-Yi, Chen Jun-Hua, Zhang Peng-Fei, He Rui. A theorem for quantum operator correspondence to the solution of the Helmholtz equationJ. Chin. Phys. B, 2014, 23(11): 110301.
Fan Hong-Yi, Chen Jun-Hua, Zhang Peng-Fei, He Rui. A theorem for quantum operator correspondence to the solution of the Helmholtz equationJ. Chin. Phys. B, 2014, 23(11): 110301.
|
A theorem for quantum operator correspondence to the solution of the Helmholtz equation
-
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. -
DownLoad: