The theories of stationary and time-dependent wave operators and their applications in photochemistry

This work presents different experiments of photorelaxation and photodissociation by using either time-dependent treatments based on wave packets propagation or Floquet stationnary matrix theory. Our treatment makes a partioning of the dynamics space explored by the evolution operator and simplifies the relaxation scheme inferred from the Schrödinger equation. The choice of these subspaces and the building up of the effective Hamiltonians which govern the projected dynamics are carried out using Bloch time-dependent or time-independent wave operators technique. The basic equations which feature these wave operators are given. The different recursive solutions based on Jacobi and Gauss-Seidel integration schemes are also included. It is noteworthy that these recent methods can be used to study molecular systems including large basis sets (their dimension may be more than 10⁵ ) and even Hamiltonians dependent explicitly on time. A complete analysis is made of the phenomenon of molecular or electromagnetic field induced resonances. This analysis shows the major role of these resonances in photodissociation processes, raises up the problem linked to their representation on a finite basis set and the difficulties inherent in using time-dependent treatment for scattering experiments.