  A presentation and a generalisation are given of the phenomenon of level
rearrangement, which occurs when an attractive long-range potential is
supplemented by a short-range attractive potential of increasing strength. This
problem has been discovered in condensate-matter physics and has also been
studied in the physics of exotic atoms. A similar phenomenon occurs in a
situation inspired by quantum dots, where a short-range interaction is added to
an harmonic confinement.
