"kick" from the electromagnetic field, that "excite" the electron. This event occurs at an arbitrary time that uni-vocally characterizes the quantum path . A final evolution driven by both the field and the Coulomb potential, given by . In parallel, you also have a quantum path that do not perceive the field at all, this trajectory is indicated by the right-hand side term in Eq. . This process is entirely time-reversible, i.e. can also occur in the opposite order. Equation is not straightforward to handle. However, physicists use it as the starting point for numerical calculation, more advanced discussion or several approximations. For strong-field interaction problems, where ionization may occurs, one can imagine to project Eq. in a certain continuum state (unbounded state or free state) , of momentum , so that: is the probability amplitude to find at a certain time , the electron in the continuum states . If this probability amplitude is greater than zero than the electron is photo-ionized. For the majority of application, the second term in is not considered, and only the first one is used in discussions, hence: Equation is also known as time reversed S-matrix amplitude and it gives the probability of photo-ionization by a generic time-varying electric field. Strong field approximation (SFA) Strong field approximation (SFA), or Keldysh-Faisal-Reiss theory is a physical model, started in 1964 by the Russian physicist Keldysh , is currently used to describe the behavior of atoms (and molecules) in intense laser fields. SFA is the starting theory for discussing both high-harmonic generation and attosecond pump-probe interaction with atoms. The main assumption made in SFA is that the free-electron dynamics is dominated by the laser field, while the Coulomb potential is regarded as a negligible perturbation. This fact re-shapes equation into: where, is the Volkov Hamiltonian, here expressed for simplicity in the velocity gauge, with , , the electromagnetic vector potential. At this point, to keep the discussion at its basic level, lets consider an atom with a single energy level , ionization energy and populated by a single electron (single active electron approximation). We can consider the initial time of the wave function dynamics as , and we can assume that initially the electron is in the atomic ground state . So that, and Moreover, we can regard the continuum states as plane wave functions state, . This is a rather simplified assumption, a more reasonable