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

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.