An alternative formalism that diagonalizes the system Hamiltonian in e
ver-larger boxes is shown to yield, for any Hermitian Hamiltonian and
in particular a time-periodic Hamiltonian, all the observables sought
by generic non-L2 full-scattering and half-scattering methods. No comp
lex potential, coordinate rotations, or solutions of coupled equations
are necessary. All observable quantities are computed from the same s
et of diagonalizations. A model Floquet problem is treated.