The principal aim of this paper is to derive an abstract form of the third Green identity associated with a proper extension $T$ of a symmetric operator $S$ in a Hilbert space $\mathfrak H$, employing the technique of quasi boundary triples for $T$. The general results are illustrated with couplings of Schr\"{ o}dinger operators on Lipschitz domains on smooth, boundaryless Riemannian manifolds.
Categories: math.AP math.SP