Stable and efficient momentum-space solutions of the time-dependent Schrödinger equation for one-dimensional atoms in strong laser fields

One-dimensional model systems have a particular role in strong-field physics when gaining physical insight by computing data over a large range of parameters, or when performing numerous time propagations within, e.g., optimal control theory. Here we derive a scheme that removes a singularity in the one-dimensional Schrodinger equation in momentum space for a particle in the commonly used soft-core Coulomb potential. By using this scheme we develop two numerical approaches to the time-dependent Schrodinger equation in momentum space. The first approach employs the expansion of the momentum-space wave function over the eigenstates of the field-free Hamiltonian, and it is shown to be more efficient for laser parameters usual in strong field physics. The second approach employs the Crank-Nicolson scheme or the method of lines for time-propagation. The both methods are readily applicable for large-scale numerical simulations in one-dimensional model systems.

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