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

作者：Fan Hong-Yi^*; Chen Jun-Hua; Zhang Peng-Fei; He Rui

来源：Chinese Physics B, 2014, 23(11): 110301.

DOI：10.1088/1674-1056/23/11/110301

• normally ordered expansion
• radius operators
• Helmholtz equation
• Bessel operator function

We propose a theorem for the quantum operator that corresponds to the solution of the Helmholtz equation, i. e., @@@ integral integral integral V (x(1),x(2),x(3)) vertical bar x(1),x(2),x(3)) < x(1),x(2),x(3)> d(3)x = V (X-1,X-2,X-3) = e(-lambda 2)/4 : V (X-1,X-2,X-3) :, @@@ where V (x(1), x(2), x(3)) is the solution to the Helmholtz equation del V-2 + lambda V-2 = 0, the symbol : : denotes normal ordering, and X-1, X-2, X-3 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.

• 出版日期2014-11
• 单位皖西学院; 中国科学技术大学; 宁波大学