STATIONARY SOLUTIONS FOR AN ELECTRON IN AN INTENSE LASER FIELD .2. MULTIMODE CASE

The Schrodinger equation for an electron and a multimode photon field with interactions is solved in the large-photon-number limit by using an 'integration' method. A graphical technique different from Feynman's is developed to represent the terms in the solution. By this graphical technique, all interactions between the electron and the multimode photon field are evaluated to any arbitrary order according to the number of transferred photons. The graphical technique allows one easily to write down the wavefunctions for an electron interacting with a strong photon field which contains an arbitrary number of photon modes. The two-mode case is discussed in detail as an example. Some interesting physical questions arising from the solutions are briefly discussed. As a simple application, a direct generalization of the Keldysh-Faisal-Reiss formula for the transition rate of multiphoton ionization, is given in the case where two different laser beams are applied.