  Recently, general point interactions in one dimension has been used to model
a large number of different phenomena in quantum mechanics. Such potentials,
however, requires some sort of regularization to lead to meaningful results.
The usual ways to do so rely on technicalities which may hide important
physical aspects of the problem. In this work we present a new method to
calculate the exact Green functions for general point interactions in 1D. Our
approach differs from previous ones because it is based only on physical
quantities, namely, the scattering coefficients, $R$ and $T$, to construct $G$.
Renormalization or particular mathematical prescriptions are not invoked. The
simple formulation of the method makes it easy to extend to more general
contexts, such as for lattices of $N$ general point interactions; on a line; on
a half-line; under periodic boundary conditions; and confined in a box.
