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

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

2000-09-11

arxiv.org/abs/math-ph/0009016v2

J. Phys. A: Math. Gen. 35 (2002) 3727

Physics

Mathematical Physics

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Scientific paper

10.1088/0305-4470/35/16/311

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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