Stationary resonance state properties

Expression (170) represents the radiant character of the molecular quasi-stationary state v>. It describes how the radiant properties are distributed over the many resonant states of the molecules. If oscillator strength from the /> manifold is strictly negligible (see, however. Section III,A), the radiative width associated with the resonance Ey, is related to the radiative width of the radiant state by... 

The nature of this initially prepared excited state and its coherence properties can be simply expressed in the basis of the quasi-stationary molecular states, only for well-resolved, nonoverlapping resonances, so that... 

The understanding, interpretation and practical tools to approach the problem of resonances states in quantum chemistry and molecular physics are basically very well studied. Generally one has either (i) concentrated on the properties of the stationary time-independent scattering solution (ii) attempted to extract the Gamow wave by analytic continuation and/or (iii) considered the time-dependent problem via a suitably prepared reference function or wave-packet. In each case the analysis prompts different explanations, numerical techniques and understanding, see e.g. Ref. [15] for a review and more details. 

The first volume contained nine state-of-the-art chapters on fundamental aspects, on formalism, and on a variety of applications. The various discussions employ both stationary and time-dependent frameworks, with Hermitian and non-Hermitian Hamiltonian constructions. A variety of formal and computational results address themes from quantum and statistical mechanics to the detailed analysis of time evolution of material or photon wave packets, from the difficult problem of combining advanced many-electron methods with properties of field-free and field-induced resonances to the dynamics of molecular processes and coherence effects in strong electromagnetic fields and strong laser pulses, from portrayals of novel phase space approaches of quantum reactive scattering to aspects of recent developments related to quantum information processing. 

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