Resonance state stationary analysis

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. 

Essentially only the total 9 has a meaning, because this describes the stationary state. The splitting 9 = 91 9n is artificial and this forms only a means of finding an approximate solution of the wave equation, thus a necessary consequence of our mathematical incapacity. Resonance is therefore also not a real physical phenomenon but a human mnemonic. It is the same as when we say of a cnild, just like his mother and later just like his father . We do not really mean that the person of the child alternates, resonates , between that of mother and father or that these latter are present as parts but only that to a first approximation we try to describe his personality as a sum of two other entities. An analysis of an entity such as a human being into intelligence, character etc, can be very useful for an opinion but is not based on the presence of distinct parts which are themselves the subject of investigation. 

The independence of Hgff on the time interval of the sequence under the condition that this interval lies between T2 and Tie can be used for determining proper Heff. This approach was first used in multi-pulse nuclear magnetic resonance in paper, and later, in NQR, for the analysis of quasi-stationary state in multi-pulse spin locking in the nuclear system with the spin of 5/tF at exact resonance. We extended this approach to the arbitrary offset of the pulse carrier frequency in relation to the resonance transition. 

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