Chapter 16: Design of Femtosecond Pulse Sequences to Control Reactions
Optimal Control Theory. If any pulse shape or pulse sequence whatsoever could be crafted in the laboratory, what shape would be optimal for cleaving
a particular bond in a particular molecule? The question of finding the
optimal shape of laser pulses is naturally formulated as a problem in the calculus of variations and its close cousin, Optimal Control Theory (OCT),
which is an extension of the calculus of variations to problems with differential equation constraints.
In our case, the differential equation constraint is the Time Dependent Schrödinger equation (TDSE) in the presence of the control, which is the electric field interacting with
the transition dipole moment of the molecule.
is (shown in 
(shown in 
In general, one has to iterate the propagation until self consistency is reached be- tween 
and 
The first 10 iterations, as well as the final it- eration can be viewed by clicking on the appropriate link.