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Some Problems with the Dirac Delta Function: Divergent Series in Physics

  • General and Applied Physics
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A Correction to this article was published on 14 March 2022

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Abstract

The completeness relation for the eigenfunctions of a self-adjoint operator generally involves a divergent series or integral. In this paper, we show, using the eigenfunctions of the infinite square well as an example, that these divergent objects can be interpreted as distributions. This should be obvious since the right-hand side of these completeness relations is the Dirac delta function but the direct calculation of the right-hand side can be very laborious, but instructive.

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Acknowledgements

The authors would like to thank Professors Luiz Nunes de Oliveira and Walter Felipe Wreszinski for discussions and clarifications about the content of this paper. The authors acknowledge partial financial support from CNPq.

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Authors and Affiliations

  1. Faculdade de Medicina, Universidade de São Paulo e LIM 01-HCFMUSP, 05405-000, São Paulo, SP, Brasil

    Marcos Amaku, Francisco A. B. Coutinho & Eduardo Massad

  2. Faculdade de Medicina Veterinária e Zootecnia, Universidade de São Paulo, 05508-970, São Paulo, SP, Brasil

    Marcos Amaku

  3. Instituto de Física, Universidade de São Paulo, 05508-970, São Paulo, SP, Brasil

    Oscar J. P. Éboli

  4. Fundação Getúlio Vargas, Rio de Janeiro, RJ, Brazil

    Eduardo Massad

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  1. Marcos Amaku
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  2. Francisco A. B. Coutinho
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  3. Oscar J. P. Éboli
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  4. Eduardo Massad
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Correspondence to Oscar J. P. Éboli.

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Amaku, M., Coutinho, F.A.B., Éboli, O.J.P. et al. Some Problems with the Dirac Delta Function: Divergent Series in Physics. Braz J Phys 51, 1324–1332 (2021). https://doi.org/10.1007/s13538-021-00916-5

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  • DOI: https://doi.org/10.1007/s13538-021-00916-5

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