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In this paper we prove the existence of orbitally stable standing waves forthe 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 theassociated energy. Moreover, we discuss the case of the presence of a Hardyenergy term, in conjunction with the behavior of the standing waves at thesingularity.

Orbital Stability for the Schr\"{o}dinger Operator Involving Inverse Square Potential