Quantum Transitions Interaction Picture

Having discussed the quantum evolution in terms of unitary and statistical operators we can make the further step towards describing quantum transitions. The starting point stays, as already custom with, on the unitary evolution action on given initial state  

With the help of this temporal statistic operator one may write the average of an observable A, in a given representation 1 )) = ZJ )( on selected state 11) of a measurement as  

Other properties will be unfolded later with the occasion of density matrix quantum formalism. For the moment we use this operatorial property to 

Quantum Nanochemistry-Volume I Quantum Theory and Observability 

Worth remarking that, the statistical operator takes the crucial role in carrying the entirely quantum evolution, from initial state to the end. In this respect, there seems it may hidden an even more crucial information 

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The slowness of the nuclear motion results (in the time-dependent picture) in a small change of the electron-nuclear interaction during the electronic time Te = (ACg )- -, where Aee is the separation of electronic states. The probability of a transition from a nondegenerate electronic state to an excited state is exponentially small. Thus, the quantum numbers n and v are essentially integrals of motion. 

Figure 2 Spectrum of the J = 8-7 rotational transition of I32xe65cu35ci xiig complicated hyperfine structure arises from nuclear quadrupole interactions of Cu (7cu = 3/2) and Cl (Id = 3/2). All transitions are split into Doppler doublets as a result of the molecular expansion traveling parallel to the microwave cavity axis. For clarity of the picture, the quantum number assignments of only a few hyperfine components are given as F -F". The...

Figure 2 Spectrum of the 7 = 8-7 rotational transition of Xe Cu Cl. The compUcated hyperfine structure arises from nuclear quadrupole interactions of Cu (7cu = 3/2) and C1 (7qi = 3/2). All transitions are spUt into Doppler doublets as a result of the molecular expansion traveling parallel to the microwave cavity axis. For clarity of the picture, the quantum number assignments of only a few hyperfine components are given as Fj -F/, F -F". The angular momentum coupling scheme Fi = Icu + J F = Fi + Iq was used. The compound was produced using laser ablation of a copper rod in a molecular expansion of a mixture of 0.1% CI2, 15% Xe, and 85% Ar. The particular isotopomer was measured in its natural abundance of 6.3%. This spectmm was recorded using 15 000 averaging cycles with a total accumulation time of about 3.5 h...

It should be stressed that the wave-packet picture of photophysical relaxation and photochemical reaction dynamics described in this chapter is substantially different from the traditional concepts in this area. In contrast to the established picture of radiationless transitions in terms of interacting tiers of zero-order molecular eigenstates, the dynamics is rationalized in terms of local properties of PE surfaces such as slopes, barriers and surface intersections, a view which now becomes widely accepted in photochemistry. This picture is firmly based on ah initio electronic-structure theory, and the molecular relaxation d3mamics is described on the basis of quantum mechanics, replacing previously prevaUing kinetic models of electronic decay processes. Such a more detailed and rigorous description of elementary photochemical processes appears timely in view of the rich and specific information on ultrafast chemical processes which is provided by modern time-resolved spectroscopy. " ... 

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