Study of Bose–Einstein condensate in the presence of the extended uncertainty principle: infinite potential well

Abstract

This paper investigates the influence of the extended uncertainty principle (EUP) and non-linearity on Bose-Einstein condensate (BEC) confined within an infinite potential well, described by a deformed one-dimensional Gross-Pitaevskii equation (GPE). Exact solutions are derived, and the impact of the EUP and the parameter of interaction g is explored through solution, position and momentum uncertainties plots. The study reveals significant changes in the probability density and energy spectra, depending on the deformation and non-linearity parameters.