We consider the ground state and the low-energy excited states of a system of
    $N$ identical bosons with interactions in the mean-field scaling regime. For
    the ground state, we derive an Edgeworth expansion for the fluctuations of
    bounded one-body operators, which yields corrections to a central limit theorem
    to any order in $1/\sqrt{N}$ . For suitable excited states, we show that the
    limiting distribution is a polynomial times a normal distribution, and that
    higher order corrections are given by an Edgeworth-type expansion.

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