Abstract: The relativistic equation of motion for the electron in the laser field is solved analytically by use of the Hamihon-Jacobi method. For a given arbitrary elliptically polarized laser field, we obtain the exact analytical expressions in the case of the laboratory frame where the laser and the electron meet collinearly, the frame where the electron is initially at rest and the frame where the electron is on the average at rest, respectively.

Key words: vector potential, Hamilton-Jacobi equation, boundary condition, equation of motion