We develop a nonperturbative model for the response of atomic electrons to oscillating external electric fields, valid in the physical regime where the central electric force is well described by an inverse square law and where the driven oscillations preserve the principal quantum number. We use the model to calculate the odd-harmonic electric-dipole radiation from a single atom driven by a laser field. The exact time-dependent eigensolutions of the model illustrate Zel’dovich’s concept of quasi-energy for sinusoidally time-dependent Hamiltonians. The validity and applicability of the model and suggested improvements are briefly discussed.