The aim of this paper is two folded. Firstly, we study the validity of the
Pohozaev-type identity for the Schr\"{o}dinger operator $$A_\la:=-\D
-\frac{\la}{|x|^2}, \q \la\in \rr,$$ in the situation where the origin is
located on the boundary of a smooth domain $\Omega\subset \rr^N$, $N\geq 1$.
The problem we address is very much related to optimal Hardy-Poincar\'{e}
inequality with boundary singularities which has been investigated in the
recent past in various papers. In view of that, the proper functional framework
is described and explained.

Secondly, we apply the Pohozaev identity not only to study semi-linear
elliptic equations but also to derive the method of multipliers in order to
study the exact boundary controllability of the wave and Schr\"{o}dinger
equations corresponding to the singular operator $A_\la$. In particular, this
complements and extends well known results by Vanconstenoble and Zuazua [34],
who discussed the same issue in the case of interior singularity.