  This paper is devoted to the inverse problem of recovering simultaneously a
potential and a point source in a Shr\"odinger equation from the associated
nonlinear Dirichlet to Neumann map. The uniqueness of the inversion is proved
and logarithmic stability estimates are derived. It is well known that the
inverse problem of determining only the potential while knowing the source, is
ill-posed. In contrast the problem of identifying a point source when the
potential is given is well posed. The obtained results show that the nonlinear
Dirichlet to Neumann map contains enough information to determine
simultaneously the potential and the point source. However recovering a point
source imbedded in an unknown background medium becomes an ill-posed inversion.
