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Shannon entropy and interference in the double-slit experiment with matter waves

Departamento de Física, Universidade Federal do Piauí, Campus Ministro Petrônio Portela, CEP 64049-550, Teresina, PI, Brazil

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L. S. Marinho

Departamento de Física, Universidade Federal do Piauí, Campus Ministro Petrônio Portela, CEP 64049-550, Teresina, PI, Brazil

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H. A. S. Costa

Departamento de Física, Universidade Federal do Piauí, Campus Ministro Petrônio Portela, CEP 64049-550, Teresina, PI, Brazil

E-mail Address: helderfisica@gmail.com

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Marcos Sampaio

Departamento de Física, Instituto de Ciências Exatas, Universidade Federal do ABC, Av. dos Estados, 5001 – Bangú, Santo André 09210-580, São Paulo, Brazil

E-mail Address: marcos.sampaio@ufabc.edu.br

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, and

I. G. da Paz

Departamento de Física, Universidade Federal do Piauí, Campus Ministro Petrônio Portela, CEP 64049-550, Teresina, PI, Brazil

E-mail Address: irismarpaz@ufpi.edu.br

Corresponding author

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https://doi.org/10.1142/S0217732319500172Cited by:4 (Source: Crossref)

Abstract

The Shannon entropy has been used to study the localization/delocalization of a distribution for different systems. Greater increased localization was associated with the smaller values and increased delocalization with the larger values of the Shannon entropy. In this paper, we show that for the double-slit experiment in the position and momentum spaces, smaller values of the Shannon entropy are associated with larger number of interference fringes and larger values of the Shannon entropy with smaller number of interference fringes.

Keywords:

PACS: 03.65.Xp, 03.65.-w, 32.80.-a

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