  A set of exact closed-form Bloch-state solutions to the stationary
Gross-Pitaevskii equation are obtained for a Bose-Einstein condensate in a
one-dimensional periodic array of quantum wells, i.e. a square-well periodic
potential. We use these exact solutions to comprehensively study the Bloch
band, the compressibility, effective mass and the speed of sound as functions
of both the potential depth and interatomic interaction. According to our
study, a periodic array of quantum wells is more analytically tractable than
the sinusoidal potential and allows an easier experimental realization than the
Kr\"onig-Penney potential, therefore providing a useful theoretical model for
understanding Bose-Einstein condensates in a periodic potential.
