  We present a numerical formalism for solving the Lippmann-Schwinger equation
for the electric field in three dimensions. The formalism may be applied to
scatterers of different shapes and embedded in different background media, and
we develop it in detail for the specific case of spherical scatterers in a
homogeneous background medium. In addition, we show how several physically
important quantities may readily be calculated with the formalism. These
quantities include the extinction cross section, the total Green's tensor, the
projected local density of states and the Purcell factor as well as the
quasinormal modes of leaky resonators with the associated resonance frequencies
and quality factors. We demonstrate the calculations for the well-known
plasmonic dimer consisting of two silver nanoparticles and thus illustrate the
versatility of the formalism for use in modeling of advanced nanophotonic
devices.
