Present status of the many-body problem

The author reports here on some recent work that was carried out partly at A and M, which aims for a microscopic understanding of large, inhomogeneous quantum systems. The author believes that this subject is also one of the developments in modern many-body theory that is closest to the subject of the workshop. To some extent it is, of course, also necessary to review the results of other groups, mainly those who do Monte-Carlo simulations. He begins by briefly discussing the different approaches of an experimentalist and a theorist towards investigating a many-body system