In a laser field, for the electron scattered by Coulomb potential, when the wave function is expanded by Floquet partial wave, the Sehrodinger equation separates into the radial form by separation of variables. The system of equations for the radial wave function is infinitely coupling linear second order differential equations. When weak laser field is considered as a pertubation, the equations can be reduced into second order ordinary differential equations and they are integrable.The radial wave functions S-matrix and the cross section are obtained. Finally, the resonance lines appear for differential cases of polarizations no matter whether the dipole approximation is used. The resonance energies, the intensities of resonance lines are obtained.