Extracting complex resonance energies from real calculations
Résumé
The dynamics of quantum resonances, their energies and their widths, are investigated by means of time-dependent unitary and non-unitary transformations of the Hamiltonian. The aim of the change of representation of the Schrödinger equation is to shape the wave function of the resonances to transform non-square integrable wave functions into localized square-integrable functions. The approach has two advantages: first, it closely relates the energy of the resonances to their dynamics, second, the computational scheme should be compatible with the standard codes of quantum chemistry. The real energies are directly converted into the complex energies of the resonances by analytical continuation. The approach is applied to the discrete Fano model, to a simple model of shape resonance and to the molecular anion H-2.