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Title: The Bender-Dunne basis operators as Hilbert space operators

Abstract

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

Authors:
Publication Date:
OSTI Identifier:
22251560
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Physics
Additional Journal Information:
Journal Volume: 55; Journal Issue: 2; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; HILBERT SPACE; INTEGRALS; QUANTUM OPERATORS

Citation Formats

Bunao, Joseph, and Galapon, Eric A., E-mail: eagalapon@up.edu.ph, E-mail: eric.galapon@upd.edu.ph. The Bender-Dunne basis operators as Hilbert space operators. United States: N. p., 2014. Web. doi:10.1063/1.4863901.
Bunao, Joseph, & Galapon, Eric A., E-mail: eagalapon@up.edu.ph, E-mail: eric.galapon@upd.edu.ph. The Bender-Dunne basis operators as Hilbert space operators. United States. https://doi.org/10.1063/1.4863901
Bunao, Joseph, and Galapon, Eric A., E-mail: eagalapon@up.edu.ph, E-mail: eric.galapon@upd.edu.ph. 2014. "The Bender-Dunne basis operators as Hilbert space operators". United States. https://doi.org/10.1063/1.4863901.
@article{osti_22251560,
title = {The Bender-Dunne basis operators as Hilbert space operators},
author = {Bunao, Joseph and Galapon, Eric A., E-mail: eagalapon@up.edu.ph, E-mail: eric.galapon@upd.edu.ph},
abstractNote = {The Bender-Dunne basis operators, T{sub −m,n}=2{sup −n}∑{sub k=0}{sup n}(n/k )q{sup k}p{sup −m}q{sup n−k} where q and p are the position and momentum operators, respectively, are formal integral operators in position representation in the entire real line R for positive integers n and m. We show, by explicit construction of a dense domain, that the operators T{sub −m,n}'s are densely defined operators in the Hilbert space L{sup 2}(R)},
doi = {10.1063/1.4863901},
url = {https://www.osti.gov/biblio/22251560}, journal = {Journal of Mathematical Physics},
issn = {0022-2488},
number = 2,
volume = 55,
place = {United States},
year = {Sat Feb 15 00:00:00 EST 2014},
month = {Sat Feb 15 00:00:00 EST 2014}
}