A theoretical justification of the empirical surface hopping method for the laser-driven molecular dynamics is given utilizing the formalism of the exact factorization of the molecular wavefunction [Abedi et al., PRL 105, 123002 (2010)] in its quantum-classical limit. Employing an exactly solvable H + 2 -like model system, it is shown that the deterministic classical nuclear motion on a single timedependent surface in this approach describes the same physics as stochastic (hopping-induced) motion on several surfaces, provided Floquet surfaces are applied. Both quantum-classical methods do describe reasonably well the exact nuclear wavepacket dynamics for extremely different dissociation scenarios. Hopping schemes using Born-Oppenheimer surfaces or instantaneous Born-Oppenheimer surfaces fail completely. For more than two decades, surface hopping (SH) [1] has been among the most popular and successful methods to describe non-adiabatic phenomena in atomic manybody systems (for reviews see [2][3][4][5]). From the theoretical point of view, however, any SH scheme is inherently a phenomenological approach. The ad hoc assumption of stochastic jumps between electronic potential energy surfaces (PES) has, so far, never been rigorously deduced from the time-dependent Schrödinger equation (TDSE) for electrons and nuclei, and even the choice of the applied PES is ambiguous.Very recently, however, first attempts have been made to justify the SH methodology on Born-Oppenheimer surfaces (BOSs), solely for the laser-free non-adiabatic dynamics [6][7][8][9]. A close similarity between the exact wavepacket propagation and SH on BOSs has been found in the framework of the exact factorization of the molecular wavefunction [6]. In this theory, the so-called exact time-dependent potential energy surface (EPES), together with an exact time-dependent vector potential, governs the true nuclear wavepacket dynamics. The EPES can exhibit nearly discontinuous step-like features, just in the vicinity of avoided crossings between BOSs, leading simultaneously to acceleration and deceleration of certain parts of the quantum wavepacket and resulting in its splitting. In close analogy, the SH mechanism can create branches of classical trajectories at avoided crossings. The findings [6] justify, albeit qualitatively but anyhow convincingly, the SH methodology on BOSs, in the field-free case.For the laser-driven dynamics, any validation of SH is still lacking and the appropriate choice of the applicable PES is discussed controversially, at present [10][11][12]. In fact, the hitherto purely intuitively chosen PES in SH models are fundamentally different from each other, and include BOSs [10,[13][14][15][16][17], instantaneous BOSs (IBOSs) [18][19][20][21][22] as well as Floquet surfaces (FSs) [22][23][24]. From the massive differences in definition and properties of these PESs, one can hardly expect that the appendant SH schemes can describe the same physics. Obviously, the situation requires clarification and the general questions persist: Is ther...