• Corpus ID: 118427336

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

@article{Liu2014ASD,
  title={A self-adjoint decomposition of radial momentum implies that Dirac's introduction of the operator is insightful},
  author={Q. H. Liu and S. F. Xiao},
  journal={arXiv: Quantum Physics},
  year={2014}
}

• Q. Liu, S. Xiao
• Published 2 November 2014
• Physics
• arXiv: Quantum Physics

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.