Space-time contours to treat intense field-dressed molecular states. I. Theory

A molecular system exposed to an intense external field is considered. The strength of the field is measured by the number $L$ of electronic states that become populated during this process. In the present article the authors discuss a rigorous way, based on the recently introduced space-time contours [R. Baer, et al., J. Chem. Phys. 119, 6998 (2003)], to form $N$ coupled Schrödinger equations where $N<L$⁠, which maintains the effects due to the remaining $(L−N)$ populated states. It is shown that whereas the size of $L$ is unlimited, the main requirement concerning $N$ is that the original group of $N$ field-free states forms a Hilbert subspace in the spatial region of interest. From previous studies it is known that a group of states forms a Hilbert subspace if and only if the corresponding topological $D$ matrix is diagonal [M. Baer, et al., Farad, Discuss 127, 337 (2004)].