  Recent experimental breakthroughs in the treatment of dilute Bose gases have
renewed interest in their quantum mechanical description, respectively in
approximations to it. The ground state properties of dilute Bose gases confined
in external potentials and interacting via repulsive short range forces are
usually described by means of the Gross-Pitaevskii energy functional. In joint
work with Elliott H. Lieb and Jakob Yngvason its status as an approximation for
the quantum mechanical many-body ground state problem has recently been
rigorously clarified. We present a summary of this work, for both the two- and
three-dimensional case.
