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The non-self-adjointness of the radial momentum operator in n dimensions

Gil Paz
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Abstract

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.

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Gil Paz. 2002-04-24. The non-self-adjointness of the radial momentum operator in n dimensions. https://doi.org/10.1088/0305-4470%2F35%2F16%2F311

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