InforLorV4, PascalFrancis, Corpus, bibRecord, 000260

Finite-dimensional calculus

Identifieur interne : 000260 ( PascalFrancis/Corpus ); précédent : 000259; suivant : 000261

Finite-dimensional calculus

Auteurs : Philip Feinsilver ; René Schott

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'.

Notice en format standard (ISO 2709)

Pour connaître la documentation sur le format Inist Standard.

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A03		`1`		`@0 J. phys., A, math. theor. : (Print)`
A05				`@2 42`
A06				`@2 37`
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.`
A20				`@2 375214.1-375214.16`
A21				`@1 2009`
A23	`01`			`@0 ENG`
A43	`01`			`@1 INIST @2 577C @5 354000171067180190`
A44				`@0 0000 @1 © 2009 INIST-CNRS. All rights reserved.`
A45				`@0 17 ref.`
A47	`01`	`1`		`@0 09-0393015`
A60				`@1 P`
A61				`@0 A`
A64	`01`	`1`		`@0 Journal of physics. A, Mathematical and theoretical : (Print)`
A66	`01`			`@0 GBR`
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`
N21				`@1 285`
N44	`01`			`@1 OTO`
N82				`@1 OTO`

Format Inist (serveur)

NO :	PASCAL 09-0393015 INIST
ET :	Finite-dimensional calculus
AU :	FEINSILVER (Philip); SCHOTT (René)
AF :	Department of Mathematics, Southern Illinois University/Carbondale, IL 62901/Etats-Unis (1 aut.); IECN and LORIA, Université Henri Poincaré-Nancy 1, BP 239/54506 Vandoeuvre-lès-Nancy/France (2 aut.)
DT :	Publication en série; Niveau analytique
SO :	Journal of physics. A, Mathematical and theoretical : (Print); ISSN 1751-8113; Royaume-Uni; Da. 2009; Vol. 42; No. 37; 375214.1-375214.16; Bibl. 17 ref.
LA :	Anglais
EA :	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'.
CC :	001B00
FD :	Mécanique quantique; Représentation analytique; Opérateur
ED :	Quantum mechanics; Analytic representation; Operator
SD :	Representación analítica; Operador
LO :	INIST-577C.354000171067180190
ID :	09-0393015

Links to Exploration step

Pascal:09-0393015

Le document en format XML

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Finite-dimensional calculus

Finite-dimensional calculus

Source :

Descripteurs français

English descriptors

Abstract

Notice en format standard (ISO 2709)

Format Inist (serveur)

Links to Exploration step

Le document en format XML

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