Trial functions in variational approximations to long-wavelength scattering

Scattering from a nearly transparent sphere is used to examine how the range of validity of the Levine–Schwinger variational technique depends on the choice of trial function and, in particular, on the physics embodied in the trial function. It is found that incorporating refractive effects into the trial function permits the extension of long-wavelength approximations into shorter-wavelength regimes. This finding will be important for the successful application of recently developed variational principles for stochastic systems, particularly stochastic systems that contain a broad distribution of particle sizes.