A self-adjoint decomposition of radial momentum implies that Dirac's introduction of the operator is insightful

Q. H. Liu; S. F. Xiao

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arXiv · 1411.0203

A self-adjoint decomposition of radial momentum implies that Dirac's introduction of the operator is insightful

Q. H. Liu·S. F. Xiao

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Abstract

With acceptance of the Dirac's observation that the \textit{canonical quantization entails using Cartesian coordinates, }we examine the\textit{\ }% operator $\mathbf{e}_{r}P_{r}$ rather than $P_{r}$ itself and demonstrate that there is a decomposition of $\mathbf{e}_{r}P_{r}$ into two self-adjoint but non-commutative parts, in which one is the total momentum and another is the transverse one. This study renders the operator $P_{r}$ indirectly measurable and physically meaningful.

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Q. H. Liu, S. F. Xiao. 2014-11-02. A self-adjoint decomposition of radial momentum implies that Dirac's introduction of the operator is insightful. https://arxiv.org/abs/1411.0203

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