Representations of the dirac deltafunction

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Autor(es): dc.contributorUniversidade Estadual Paulista (UNESP)-
Autor(es): dc.creatorBlinder, S. M.-
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Descrição: dc.descriptionThe "deltafunction" was invented by P. A. M. Dirac around 1930 in order to compactly express the completeness relation in quantum mechanics. (Essentially equivalent definitions appear in earlier works of Fourier, Kirchhoff, and Heaviside.) The deltafunction is the limit of a function that grows infinitely large in an infinitesimally small region, while its integral remains normalized to 1. The deltafunction is too singular to be considered a function in the usual sense. Mathematicians have, however, accepted it as a linear functional, a "generalized function", or "distribution". The deltafunction has computational significance only when it appears under an integral sign. Its defining relation can, in fact, be written ∫f(x)δ(x)dx from -∞ to ∞= f(0) or, more generally, ∫f(x)δ(x-a)dx from -∞ to ∞= f(a). There are a number of representations of the deltafunction based on limits of a family of functions as some parameter approaches infinity (or zero). In this Demonstration, five of these representations are illustrated. You can select the parameter n to take values from 1 to 10, on its way toward infinity-
Descrição: dc.descriptionlimit of a function, integral, Dirac Deltafunction-
Descrição: dc.descriptionComponente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemática-
Publicador: dc.publisherWolfram Demonstration Project-
Relação: dc.relationRepresentationsOfTheDiracDeltafunction.nbp-
Direitos: dc.rightsDemonstration freeware using Mathematica Player-
Palavras-chave: dc.subjectDirac Deltafunction-
Palavras-chave: dc.subjectIntegrals-
Palavras-chave: dc.subjectnormalized Gaussian distribution-
Palavras-chave: dc.subjectEducação Superior::Ciências Exatas e da Terra::Matemática::Equações Diferenciais Funcionais-
Título: dc.titleRepresentations of the dirac deltafunction-
Tipo de arquivo: dc.typetexto-
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