Time dependent Schrodinger equation 8 Metal surfaces 6 Nonlinear equations 6 Numerical solution 6 Schrodinger equation 6 Ultrashort pulses 6 Band structure 4 Band-structure-based models 4 Condensed matter physics 4 Distorted waves 4 Emission spectroscopy 4 Grazing incidence 4 Photo-electron emission 4 Photoelectron spectroscopy 4 Photoelectrons 4 Photons 4 Structure-based 4 Atomic hydrogen 2 Basis sets 2 Charge-up 2 Collision problem 2 Dipolar approximations 2 Eigenvalues and eigenfunctions 2 Excitation cross section 2 Excitation mechanisms 2 Fully-quantal 2 Highly charged ions 2 Hydrogen 2 Hydrogen atoms 2 Impact-parameter 2