16. Wave Operators and Active Subspaces: Tools for the Simplified Dynamical Description of Quantum Processes Involving Many-Dimensional State Spaces
Georges Jolicard, John P. Killingbeck · Society for Industrial and Applied Mathematics eBooks · 1995
Time-dependent and stationary wave operators are presented as tools to define active spaces and simplified dynamics for the integration of the time-dependent Schrödinger equation in large quantum spaces. Within this framework a new light is thrown on the duality between time-dependent and time-independent approaches and a generalized version of the adiabatic theorem is given. For the Floquet treatment of photodissociation processes, the choice of the relevant subspaces and the construction of the effective Hamiltonians are carried out using the Bloch wave operator techniques. Iterative solutions of the basic equations associated with these wave operators are given, based on Jacobi, Gauss-Seidel and variational schemes.