  In this paper we prove the existence of orbitally stable standing waves for
the critical Schr\"{o}dinger operator, involving potential of the form
$\left(\frac{N-2}{2}\right)^2|x|^{-2}$. The approach, being purely variational,
is based on the precompactness of any minimizing sequence with respect to the
associated energy. Moreover, we discuss the case of the presence of a Hardy
energy term, in conjunction with the behavior of the standing waves at the
singularity.
