  The inherently homogeneous stationary-state and time-dependent Schroedinger
equations are often recast into inhomogeneous form in order to resolve their
solution nonuniqueness. The inhomogeneous term can impose an initial condition
or, for scattering, the preferred permitted asymptotic behavior. For bound
states it provides sufficient focus to exclude all but one of the homogeneous
version's solutions. Because of their unique solutions, such inhomogeneous
versions of Schroedinger equations have long been the indispensable basis for a
solution scheme of successive perturbational corrections which are anchored by
their inhomogeneous term. Here it is noted that every such perturbational
solution scheme for an inhomogeneous linear vector equation spins off a
nonperturbational continued-fraction scheme. Unlike its
representation-independent antecedent, the spin-off scheme only works in
representations where all components of the equation's inhomogeneous term are
nonzero. But that requirement seems to confer theoretical physics robustness
heretofore unknown: for quantum fields the order of the perturbation places a
bound on unperturbed particle number, the spin-off scheme contrariwise has only
basis elements of unbounded unperturbed particle number. It furthermore is
difficult to visualize such a continued-fraction spin-off scheme generating
infinities, since its successive iterations always go into denominators.
