Abstract
Bose-Einstein condensates (BECs) comprise a state of matter in which separate atoms or subatomic particles coalesce into a single macroscopic wave function when cooled to near absolute zero. BECs are confined within traps when carrying out experiments, and in the present paper, we model BECs confined within three-dimensional infinite potential wells corresponding to impenetrable boxes with prescribed geometric properties. To do this, we study the Gross-Pitaevskii equation (GPE) governing the macroscopic wave function within generic three-dimensional finite boxes, first describing analytical and numerical approaches for solving the ground state macroscopic wave function, and then employing these methods to understand how the geometry of a confining box influences properties of the BEC wave function. We show that the chemical potential of the BEC is sensitive to the size and shape of the box, with the chemical potential lowest for a spherical box and comparatively large for boxes with more extreme aspect ratios. Compared to commonly employed harmonic traps, geometrically confined BECs exhibit larger variations of the chemical potential with the self-interaction parameter, yet geometrically confined attractive BECs may be more robust against collapse. In particular, we show that the collapse threshold for an attractive BEC can be modified by the specific manner of geometric confinement.