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arXiv · 1509.00340

The Bender-Dunne basis operators as Hilbert space operators

Joseph Bunao·Eric Galapon
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Abstract

The Bender-Dunne basis operators, $\mathsf{T}_{-m,n}=2^{-n}\sum_{k=0}^n {n \choose k} \mathsf{q}^k \mathsf{p}^{-m} \mathsf{q}^{n-k}$ where $\mathsf{q}$ and $\mathsf{p}$ are the position and momentum operators respectively, are formal integral operators in position representation in the entire real line $\mathbb{R}$ for positive integers $n$ and $m$. We show, by explicit construction of a dense domain, that the operators $\mathsf{T}_{-m,n}$'s are densely defined operators in the Hilbert space $L^2(\mathbb{R})$.

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Joseph Bunao, Eric Galapon. 2015-09-01. The Bender-Dunne basis operators as Hilbert space operators. https://doi.org/10.1063/1.4863901

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