InforLorV4, PascalFrancis, Curation, bibRecord, 000767

Finite-dimensional calculus

Identifieur interne : 000767 ( PascalFrancis/Curation ); précédent : 000766; suivant : 000768

Finite-dimensional calculus

Auteurs : Philip Feinsilver [États-Unis] ; René Schott [France]

Source :

Journal of physics. A, Mathematical and theoretical : (Print) [ 1751-8113 ] ; 2009.

RBID : Pascal:09-0393015

Descripteurs français

Pascal (Inist)
- Mécanique quantique, Représentation analytique, Opérateur.

English descriptors

KwdEn :
- Analytic representation, Operator, Quantum mechanics.

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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A05				`@2 42`
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A08	`01`	`1`	`ENG`	`@1 Finite-dimensional calculus`
A11	`01`	`1`		`@1 FEINSILVER (Philip)`
A11	`02`	`1`		`@1 SCHOTT (René)`
A14	`01`			`@1 Department of Mathematics, Southern Illinois University @2 Carbondale, IL 62901 @3 USA @Z 1 aut.`
A14	`02`			`@1 IECN and LORIA, Université Henri Poincaré-Nancy 1, BP 239 @2 54506 Vandoeuvre-lès-Nancy @3 FRA @Z 2 aut.`
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C01	`01`		`ENG`	@0 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'.
C02	`01`	`3`		`@0 001B00`
C03	`01`	`3`	`FRE`	`@0 Mécanique quantique @5 26`
C03	`01`	`3`	`ENG`	`@0 Quantum mechanics @5 26`
C03	`02`	`X`	`FRE`	`@0 Représentation analytique @5 27`
C03	`02`	`X`	`ENG`	`@0 Analytic representation @5 27`
C03	`02`	`X`	`SPA`	`@0 Representación analítica @5 27`
C03	`03`	`X`	`FRE`	`@0 Opérateur @5 28`
C03	`03`	`X`	`ENG`	`@0 Operator @5 28`
C03	`03`	`X`	`SPA`	`@0 Operador @5 28`
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<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>
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Finite-dimensional calculus

Finite-dimensional calculus

Source :

Descripteurs français

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Abstract

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