Quantum electrodynamic approach to the Volkov-Coulomb problem

We have previously presented a nonperturbative quantum electrodynamic appro ach to the atom-light system, and solved it by nonperturbative treatment li mited to the electron-photon interactions only. In this paper, we solve the equation of motion, a time-independent Schrodinger like equation for the c ombined atom-photon-mode system, nonperturbatively for both the atomic Coul omb potential and the photon mode, by employing a Born-Oppenheimer approxim ation in momentum space. The solution obtained is the direct product of a p hotonic part, representing a stimulated photon cloud dressing the electron, and an electronic part, as if the atomic potential is distorted. For atoms with known spectra and wavefunctions, the integral equation for the distor ted atomic wavefunctions is reduced to a solvable set of linear algebraic e quations with explicitly determined coefficients. Applications of this resu lt are also discussed.