Title

The Bender-Dunne basis operators as Hilbert space operators

College

College of Science

Department/Unit

Physics

Document Type

Article

Source Title

Journal of Mathematical Physics

Volume

55

Issue

022102-1

Publication Date

2014

Abstract

The Bender-Dunne basis operators, ๐–ณโˆ’m,n=2โˆ’nโˆ‘nk=0(nk)๐—Šk๐—‰โˆ’m๐—Šnโˆ’kTโˆ’m,n=2โˆ’nโˆ‘k=0nnkqkpโˆ’mqnโˆ’k where ๐—Šq and ๐—‰p are the position and momentum operators, respectively, are formal integral operators in position representation in the entire real line โ„R for positive integers n and m. We show, by explicit construction of a dense domain, that the operators ๐–ณโˆ’m,nTโˆ’m,n's are densely defined operators in the Hilbert space L2(โ„)L2(R).

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Disciplines

Other Mathematics | Physics

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