On the Radial Momentum Operator

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Abstract
The validity of the radial momentum operator as an observable equivalent is investigated. In addition to the fundamental mathematical prescription, purely physical arguments are presented which demonstrate its inadmissibility. This remains in spite of its correct commutator relationship with the radial coordinate. In the course of presenting these arguments, the condition r1/2Ψ(r)←0, r←0, is derived to be a necessary condition that Ψ be an acceptable wave function.

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