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.
- Pub Date:
- October 2000
- Mathematical Physics;
- Mathematics - Mathematical Physics;
- Primary 81V70;
- Secondary 35Q55;
- For the proceedings of the International Conference on Partial Differential Equations, Clausthal, July 24-28, 2000