Time Scaling and Momentum Space Models in Intense Fields
The Time Dependent Schrödinger Equation (TDSE) in momentum space provides a very useful alternative to the coordinate representation to describe atomic and molecular processes in an intense laser field. We wish to solve this equation in the very low frequency limit.
Taking a model in which the kernel of the nonlocal Coulomb potential in momentum space is replaced by a finite sum of separable potentials each supporting one bound state of atomic hydrogen, we have cast the kernel for the resultant integral equation in a form which is a sum of a pole term and an integral with has a rapidly decaying integrand which is smooth and doesn’t oscillate making it easy to evaluate numerically. We showed that in the limit of the frequency going to zero the pole term doesn’t contribute and we expect the integral to be strongly peaked making it possible to easily solve the integral equation.
We are now in a position to study semi-analytically the limit as the frequency of the laser goes to zero which would be impossible to do by solving the TDSE as the pulse length becomes extremely long. In this way we should be able to obtain new insights into the low energy structure (LES) found in both atoms and molecules in intense fields.