  For tracing the spatiotemporal evolution of electronic systems, we suggest
and analyze theoretically a setup that exploits the excellent spatial
resolution based on scanning tunneling microscopy techniques combined with the
temporal resolution of femtosecond pump-probe photoelectron spectroscopy. As an
example, we consider the laser-induced, local vibrational dynamics of a
surface-adsorbed molecule. The photoelectrons released by a laser pulse can be
collected by the scanning tip and utilized to access the spatiotemporal
dynamics. Our proof-of-principle calculations are based on the solution of the
time-dependent Schrooedinger equation supported by the ab initio computation of
the matrix elements determining the dynamics.
