The Schrodinger-like Equation for a Nonrelativistic Electron in a Photon   Field of Arbitrary Intensity
  The ordinary Schrodinger equation with minimal coupling for a nonrelativistic electron interacting with a single-mode photon field is not satisfied by the nonrelativistic limit of the exact solutions to the corresponding Dirac equation. A Schrodinger-like equation valid for arbitrary photon intensity is derived from the Dirac equation without the weak-field assumption. The "eigenvalue" in the new equation is an operator in a Cartan subalgebra. An approximation consistent with the nonrelativistic energy level derived from its relativistic value replaces the "eigenvalue" operator by an ordinary number, recovering the ordinary Schrodinger eigenvalue equation used in the formal scattering formalism. The Schrodinger-like equation for the multimode case is also presented. 
Dong-Sheng Guo and R.R. Freeman (Lawenrence Livermore National   Laboratory) and Yong-Shi Wu (Institute for Advanced Study)