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.
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