  We study the properties of an atomic Bose--Einstein condensate produced in an
optical-box potential, using high-resolution Bragg spectroscopy. For a range of
box sizes, up to $70~\mu$m, we directly observe Heisenberg-limited momentum
uncertainty of the condensed atoms. We measure the condensate interaction
energy with a precision of $k_B \times 100$ pK and study, both experimentally
and numerically, the dynamics of its free expansion upon release from the box
potential. All our measurements are in good agreement with theoretical
expectations for a perfectly homogeneous condensate of spatial extent equal to
the size of the box, which also establishes the uniformity of our optical-box
system on a sub-nK energy scale.
