Attosecond electron dynamics: A multiresolution approach

We establish a numerical solution to the time-dependent Schrödinger equation employing an adaptive, discontinuous spectral element basis that automatically adjusts to the requested precision. The explicit time evolution is accomplished by a band-limited, gradient-corrected, symplectic propagator and uses separated representations of operators for efficient computation in multiple dimensions. We illustrate the method calculating accurate bound and continuum transition probabilities along with the photoelectron spectra for H(1s), He ⁺(1s), and Li2 ⁺(2s) in three dimensions and H ₂ ⁺ in three and four dimensions under a two-cycle attosecond laser pulse with driving frequency of 36 eV and an intensity of 1×1015W/cm2.