Numerical solution of the time-dependent Schrödinger equation for H_{2}^{+} ion with application to high-harmonic generation and above-threshold ionization.

Time evolution of the bound state of a molecular hydrogen cation in an intense, linearly polarized laser field is investigated by solving the full three-dimensional time-dependent Schrödinger equation. Our method is based on the Born-Oppenheimer and dipole approximations, and the wave function is expanded in finite series using B-spline functions and spherical harmonics in prolate spheroidal coordinates. After solving the stationary Schrödinger equation, the initial state is propagated under the influence of the laser field employing the Crank-Nicolson propagator. Using this method we calculate and present high-harmonic photon spectra and above-threshold ionization angle-resolved electron spectra.