The non-self-adjointness of the radial momentum operator in n dimensions
The non-self-adjointness of the radial momentum operator in n dimensions
复制标题
DOI：
10.1088/0305-4470/35/16/311
复制
发表时间：
2000-09
期刊：
影响因子：
--
通讯作者：
G. Paz
中科院分区：
文献类型：
--
作者：
G. Paz
径向动量算符的非自伴性以前曾被一些作者注意到，但各种证明都是不正确的。我们给出了一个严格的证明，$n$维径向动量算子不是自伴的，没有自伴扩张。证明的主要思想是证明这个算子酉等价于$L^{2}[（0，\infty），dr]$上的动量算子，它不是自伴的，也没有自伴扩张。
The non self-adjointness of the radial momentum operator has been noted before by several authors, but the various proofs are incorrect. We give a rigorous proof that the $n$-dimensional radial momentum operator is not self- adjoint and has no self-adjoint extensions. The main idea of the proof is to show that this operator is unitarily equivalent to the momentum operator on $L^{2}[(0,\infty),dr]$ which is not self-adjoint and has no self-adjoint extensions.