Extraction of eigenstates from an optically prepared state by a time-dependent quantum-mechanical method. Toward simulation of "intermediate case" radiationless transitions

We provide a method to simulate "intermediate case" radiationless transitions for given potentials. The main step is to extract eigenfunctions from an optically prepared state at a time just after the pump pulse has decayed. We generate Lanczos vectors, from the prepared state, with an energy-filtered Hamiltonian and diagonalize the unfiltered Hamiltonian. Preliminary calculations are performed. For a system of two vibrational degrees of freedom, an accuracy of 10^-5 cm^-1 can easily be obtained: the long time dynamics up to ≈ 1 μs is within reach.