  It is known that the Jost-function formulation of quantum scattering theory
can be applied to classical problems concerned with the scattering of a plane
scalar wave by a medium with a spherically symmetric inhomogeneity of finite
extent. This technique is applied to solve the radial differential equation for
the scattering from a constant spherical inhomogeneity and a piecewise constant
by two-layer spherical inhomogeneity. This could represent a spherical
scatterer with a piecewise increasing or decreasing refractive index, for
example. When the problem cannot be solved analytically in closed form, the
Jost integral formula can be used to convert it into an integral equation with
the corresponding boundary conditions.
