InforLorV4, Main, Exploration, bibRecordById, Pascal:09-0393015

Finite-dimensional calculus

Identifieur interne : 003956 ( Main/Exploration ); précédent : 003955; suivant : 003957

Finite-dimensional calculus

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

Source :

Journal of Physics A Mathematical and Theoretical [ 1751-8113 ] ; 2009.

RBID : ISTEX:C4ACD704C3D937AD1E9C7959EA389BA072326DCD

Descripteurs français

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

English descriptors

KwdEn :
- Analytic representation, Operator, Quantum mechanics.
Teeft :
- Algebra, Analytic representations, Appell system, Binomial distribution, Calculus, Canonical, Canonical appell system, Canonical commutation relations, Canonical polynomials, Canonical variables, Column vector, Commutation, Commutation relations, Commutation rule, Corresponding polynomial, Cosh, Current work, Dual vector, Feinsilver, Gegenbauer polynomials, Hilbert space, Image analysis, Krawtchouk, Krawtchouk expansion, Krawtchouk expansions, Krawtchouk ghosts, Krawtchouk polynomials, Math, Matrix, Matrix approach, Negative jumps, Nite operator calculus, Operator calculus, Orthofermion algebra, Other words, Phys, Polynomials orthogonal, Probability theory, Quantum information, Quantum mechanics, Recurrence relation, Schott, Sech, Special functions, Tanh, Theor, Vacuum state, Vector space.
mix :
- Heisenberg-Weyl algebra, inversion formulas, orthofermions, polynomial systems.

Abstract

We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated HeisenbergWeyl 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 HeisenbergWeyl 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 HeisenbergWeyl 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.

Url:

DOI: 10.1088/1751-8113/42/37/375214

Affiliations:

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Finite-dimensional calculus

Finite-dimensional calculus

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Descripteurs français

English descriptors

Abstract

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