  We present a pedagogical introduction to Bose-Einstein condensation in traps
with spherical symmetry, namely the spherical box and the thick shell,
sometimes called bubble trap. In order to obtain the critical temperature for
Bose-Einstein condensation, we describe how to calculate the cumulative state
number and density of states in these geometries, using numerical and
analytical (semi-classical) approaches. The differences in the results of both
methods are a manifestation of Weyl's theorem, i.e., they reveal how the
geometry of the trap (boundary condition) affects the number of the eigenstates
counted. Using the same calculation procedure, we analyzed the impact of going
from three-dimensions to two-dimensions, as we move from a thick shell to a
two-dimensional shell. The temperature range we obtained, for most commonly
used atomic species and reasonable confinement volumes, is compatible with
current cold atom experiments, which demonstrates that these trapping
potentials may be employed in experiments.
