Finite-dimensional calculus
Identifieur interne : 000242 ( PascalFrancis/Checkpoint ); précédent : 000241; suivant : 000243Finite-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><inist><standard h6="B"><pA><fA01 i1="01" i2="1"><s0>1751-8113</s0></fA01><fA03 i2="1"><s0>J. phys., A, math. theor. : (Print)</s0></fA03><fA05><s2>42</s2></fA05><fA06><s2>37</s2></fA06><fA08 i1="01" i2="1" l="ENG"><s1>Finite-dimensional calculus</s1></fA08><fA11 i1="01" i2="1"><s1>FEINSILVER (Philip)</s1></fA11><fA11 i1="02" i2="1"><s1>SCHOTT (René)</s1></fA11><fA14 i1="01"><s1>Department of Mathematics, Southern Illinois University</s1><s2>Carbondale, IL 62901</s2><s3>USA</s3><sZ>1 aut.</sZ></fA14><fA14 i1="02"><s1>IECN and LORIA, Université Henri Poincaré-Nancy 1, BP 239</s1><s2>54506 Vandoeuvre-lès-Nancy</s2><s3>FRA</s3><sZ>2 aut.</sZ></fA14><fA20><s2>375214.1-375214.16</s2></fA20><fA21><s1>2009</s1></fA21><fA23 i1="01"><s0>ENG</s0></fA23><fA43 i1="01"><s1>INIST</s1><s2>577C</s2><s5>354000171067180190</s5></fA43><fA44><s0>0000</s0><s1>© 2009 INIST-CNRS. 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