## 1 Introduction  
In the past two decades, the development of state-of-the-art technologies for generating and controlling ultra-short intense laser pulses has paved the way for more profound insights into electron and nuclear dynamics in atoms and molecules on their natural timescales [1; 2; 3; 4; 5]. Current theoretical treatments largely focus on electronic dynamics. However, recent experiments have demonstrated the retrieval of bond distances in simple diatomic molecules [6] and control over the ultrafast dissociation process and resolution of bond dynamics of a polyatomic molecule using laser-induced electron diffraction (LIED) [7]. To fully understand molecular dynamics during interaction with a strong laser pulse, it is therefore essential to develop a theory that takes into account the bond dynamics and dissociation process and thereby accurately describes nuclear, as well as electronic, motion. This is the aim of the present work. Among a wide variety of computational methods, one of the most applicable and important approaches is the direct solution of the time-dependent Schrodinger equation (TDSE). This approach is implementable for simulating systems with a limited number of particles in a limited region of momentum or coordinate space. There are different TDSE approaches for simulating the electron dynamics in an atomic or molecular laser-induced system in one, two, or three (full) coordinate (or momentum) dimensions [8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22]. Some of the TDSE approaches treat the nuclei in the laser-induced system dynamically using classical or quantum mechanics. Currently, it is not feasible to simulate multi-electron systems by applying the exact TDSE. To this aim, one should implement the single-active-electron approximation. To study a multi-electron system, one could also develop and evaluate other approximate methods, such as the time-dependent density functional theory (TDDFT) [23], the multiconfiguration time-dependent Hartree-Fock (MCTDHF) [24], the multiconfiguration time-dependent Hartree (MCTDH) [25], and the time dependent Hartree-Fock(TDHF) [26]. During the last two decades, a number of approaches have been developed to solve the TDSE for high-dimensional quantum systems in the presence of an ultra-short intense laser field on the basis of coherent states (CSs) and to investigate related phenomena [27; 28; 29; 30; 31; 32]. CSs have many advantageous features. First of all, their initial basis set can be generated randomly. Secondly, the Coulombic potential singularities are removed and replaced by the complex error function on the basis of CSs. Finally, on the basis of CSs, fewer configurations are needed for solving the TDSE of a system with high number of degrees of freedom. By implementing CSs for solving the TDSE, [PERSON] et al. introduced the coupled coherent states (CCS) method [27]. The CCS method was originally developed to simulate systems with distinguishable particles. For simulating fermionic systems, two different versions of a fermion coupled coherent state (FCCS) method were introduced [29; 31; 32]. The first version of the FCCS method, which was introduced by [PERSON] et al., uses a Slater determinant to symmetrize the CCS equations [29]. The second version of the FCCS method, introduced by [PERSON] et al. [31; 32], simplifies the process by (anti)symmetrizing the CSs grid, with all the governing equations the same as for the CCS method. However, the CCS method and its derivatives are essentially trajectory-guided. The most important concern regarding trajectory-guided approaches based on CCS is that they are not completely successful for real-time simulations of single- or two-electron systems in the presence of a laser field [27; 28; 29]. Here, we introduce the static coherent states (SCS) method, which can investigate the quantum electron dynamics and the classical nuclear dynamics in single- and two-electron systems in the absence or presence of an external laser field.