正径向动量算符
The positive radial momentum operator
摘要：
球坐标系中的拉普拉斯算子包含厄米正的径向动量平方算符$ p_r^2 = - r^{-1} \partial_r^2 r $。然而，正如许多作者所指出的，“径向动量算符”$ - i r^{-1} \partial_r r $不是厄米算符。找到了$ p_r^2 $的正平方根算子及其逆算子.讨论了这些算子与Fourier变换、Hilbert变换和分数次积分算子的关系。
英文摘要：
The Laplacian in spherical coordinates contains the squared radial momentum operator $ p_r^2 = - r^{-1} \partial_r^2 r $ which is Hermitian and positive. However as has been pointed out by various authors the ``radial momentum operator" $ - i r^{-1} \partial_r r $ is not Hermitian. The positive square root operator of $ p_r^2 $ is found and also its inverse. We discuss the relation of these operators with Fourier transforms, the Hilbert transform and fractional integral operators.
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