Complex scaling used to study the time evolution of a quantum system
exposed to an ultrashort laser pulse
(by Bernard Piraux)
We solve numerically the time-dependent Schrödinger equation
for one and two-electron systems exposed to ultrashort
electromagnetic pulses. Complex scaling of the Hamiltonian
is used to generate the position and the width of the doubly
excited states as well as to propagate in time the full
wavefunction of the system. We discuss in detail the two following
points. First, the physical significance of the time evolution
of the (Padé extrapolated) norm of the full wavefunction
and secondly, the photoionisation cross-section from the ground
state of helium very close but below the double ionisation threshold
of helium.