This work presents a theoretical analysis of dynamic tuning of atomic energy levels under high-frequency parametric driving. Using the Floquet-Magnus expansion within the Kramers-Henneberger (KH) frame, we derive an effective Hamiltonian for a Hydrogen atom subjected to a fast, non-ionizing oscillatory field. We show that the high-frequency quiver motion of the electron induces a time-averaged renormalization of the Coulomb potential, generating a localized contact-term correction proportional to a Dirac delta function. This perturbation selectively shifts s-orbital energy levels, which possess non-zero probability density at the nucleus, while leaving higher angular momentum states largely unaffected. As a result, the accidental degeneracy between states such as 2s and 2p is dynamically broken, producing a controllable Lamb-shift-like splitting induced by external driving. This work provides a physically grounded framework for Floquet engineering of atomic spectra, demonstrating how coherent high-frequency forcing can be used to dynamically modify quantum energy levels.
Claudia Attaianese (Tue,) studied this question.