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We consider the Schr\"{o}dinger operator $A_\l:=-\D -\l/|x|^2$, $\l\in \rr$,when the singularity is located on the boundary of a smooth domain$\Omega\subset \rr^N$, $N\geq 1$  The aim of this Note is two folded. Firstly, we justify the extension of theclassical Pohozaev identity for the Laplacian to this case. The problem weaddress is very much related to Hardy-Poincar\'{e} inequalities with boundarysingularities. Secondly, the new Pohozaev identity allows to develop themultiplier method for the wave and the Schr\"{o}dinger equations. In this waywe extend to the case of boundary singularities well known observability andcontrol properties for the classical wave and Schr\"{o}dinger equations whenthe singularity is placed in the interior of the domain (Vanconstenoble andZuazua \cite{judith}).

Hardy inequality and Pohozaev identity for operators with boundary singularities: some applications