Erlangen Programme at Large 3.2 Ladder Operators in Hypercomplex Mechanics

Abstract

We revise the construction of creation/annihilation operators in quantum mechanics based on the representation theory of the Heisenberg and symplectic groups. Besides the standard harmonic oscillator (the elliptic case) we similarly treat the repulsive oscillator (hyperbolic case) and the free particle (the parabolic case). The respective hypercomplex numbers turn out to be handy on this occasion. This provides a further illustration to the Similarity and Correspondence Principle.

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Item Type:	Article
Authors/Creators:	Kisil, VV https://orcid.org/0000-0002-6593-6147
Copyright, Publisher and Additional Information:	This is an open access article under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) (https://creativecommons.org/licenses/by/4.0/).
Keywords:	Heisenberg group; Kirillov’s method of orbits; geometric quantisation; quantum mechanics; classical mechanics; Planck constant; dual numbers; double numbers; hypercomplex; jet spaces; hyperbolic mechanics; interference; Fock-Segal-Bargmann representatio
Dates:	Published: 2011
Institution:	The University of Leeds
Academic Units:	The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds)
Depositing User:	Symplectic Publications
Date Deposited:	24 May 2019 13:05
Last Modified:	23 Jun 2023 22:22
Published Version:	https://ojs.cvut.cz/ojs/index.php/ap/article/view/...
Status:	Published
Publisher:	CTU Central Library
Related URLs:	Author
Open Archives Initiative ID (OAI ID):	oai:eprints.whiterose.ac.uk:111534

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Erlangen Programme at Large 3.2 Ladder Operators in Hypercomplex Mechanics

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