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本文主要指出B.K.Bhattacharyya和M.E.Navolio在文献[1]中将拉普拉斯方程▽~2U(x,y,z)=0进行三维傅里叶变换导出u~2+v~2+w~2=0,以及利用iw=±(u~2+v~2)~(1/2)推导了位场在频率域中的一些公式中的错误,从数学和物理角度论证这个所谓频率域的拉普拉斯方程u~2+v~2+w~2=0是不成立的。因此,当推导位场在频率域中的公式时不能使用iw=±(u~2+v~2)~(1/2)。此外,本文还使用狄拉克函数证明了拉普拉斯方程的基本解1/(x~2+y~2+z~2)~(1/2)在拉普拉斯算子作用下,在三维频率域中并没有这样的对应关系式,而只能有对应关系式
In this paper, we mainly point out that BKBhattacharyya and MENavolio derived the Laplace equation ▽ ~ 2U (x, y, z) = 0 in the literature [1] to derive u ~ 2 + v ~ 2 + w ~ 2 = 0, and using iw = ± (u ~ 2 + v ~ 2) ~ (1/2) to deduce errors in some formulas of the field in the frequency domain, and demonstrate mathematically and physically the pull of the so-called frequency domain The Plath equation u ~ 2 + v ~ 2 + w ~ 2 = 0 is not valid. Therefore, iw = ± (u ~ 2 + v ~ 2) ~ (1/2) can not be used when formulating the field in the frequency domain. In addition, the Dirac function is also used to prove that the fundamental solution 1 / (x ~ 2 + y ~ 2 + z ~ 2) ~ (1/2) of Laplace’s equation There is no such relation in the three-dimensional frequency domain, but only the corresponding relation