Inverse momentum squared in a rigged Hilbert space (RHS) and its RHS reduction
Abstract
This paper serves as an extension of our work in defining the inverse momentum operator in a rigged Hilbert space [SPP-2024-PC-25], which is the triplet Φ ⊂ H ⊂ Φ×. We construct the square of the inverse momentum as a rigged Hilbert space operator, p−2 : Φ× → Φ×, and its Hilbert space reduction, p−2|D : D → H. The particular rigging used is the Schwartz test function space. We show that D is dense in H. Moreover, we show that the RHS reduction p−2|D is unique in the Hilbert space and essentially self-adjoint.
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