  A new perspective of the Green's function in a boundary value problem as the
only eigenstate in an auxiliary formulation is introduced. In this treatment,
the Green's function can be perceived as a defect state in the presence of a
$\delta$-function potential, the height of which depends on the Green's
function itself. This approach is illustrated in one-dimensional and
two-dimensional Helmholtz equation problems, with an emphasis on systems that
are open and have a non-Hermitian potential. We then draw an analogy between
the Green's function obtained this way and a chiral edge state circumventing a
defect in a topological lattice, which shines light on the local minimum of the
Green's function at the source position.
