Finite-dimensional calculus
Identifieur interne : 003C76 ( Main/Merge ); précédent : 003C75; suivant : 003C77Finite-dimensional calculus
Auteurs : Philip Feinsilver [États-Unis] ; René Schott [France]Source :
- Journal of physics. A, Mathematical and theoretical : (Print) [ 1751-8113 ] ; 2009.
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Abstract
We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, including a review of Krawtchouk polynomials that illustrates some curious properties of the Heisenberg-Weyl algebra, as well as presenting an approach to computing Krawtchouk expansions. From a mathematical perspective, we are providing indications as to how to implement infinite terms Rota's 'finite operator calculus'.
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A, Mathematical and theoretical : (Print)</title><title level="j" type="abbreviated">J. phys., A, math. theor. : (Print)</title><idno type="ISSN">1751-8113</idno><imprint><date when="2009">2009</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Journal of physics. A, Mathematical and theoretical : (Print)</title><title level="j" type="abbreviated">J. phys., A, math. theor. : (Print)</title><idno type="ISSN">1751-8113</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Analytic representation</term><term>Operator</term><term>Quantum mechanics</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Mécanique quantique</term><term>Représentation analytique</term><term>Opérateur</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, including a review of Krawtchouk polynomials that illustrates some curious properties of the Heisenberg-Weyl algebra, as well as presenting an approach to computing Krawtchouk expansions. From a mathematical perspective, we are providing indications as to how to implement infinite terms Rota's 'finite operator calculus'.</div></front></TEI><affiliations><list><country><li>France</li><li>États-Unis</li></country><region><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Vandœuvre-lès-Nancy</li></settlement></list><tree><country name="États-Unis"><noRegion><name sortKey="Feinsilver, Philip" sort="Feinsilver, Philip" uniqKey="Feinsilver P" first="Philip" last="Feinsilver">Philip Feinsilver</name></noRegion></country><country name="France"><region name="Grand Est"><name sortKey="Schott, Rene" sort="Schott, Rene" uniqKey="Schott R" first="René" last="Schott">René Schott</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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