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 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.Comment: 26 page