Dynamical rules general solution

It should be noted that in the cases where y"j[,q ) > 0, the centroid variable becomes irrelevant to the quantum activated dynamics as defined by (A3.8.Id) and the instanton approach [37] to evaluate based on the steepest descent approximation to the path integral becomes the approach one may take. Alternatively, one may seek a more generalized saddle point coordinate about which to evaluate A3.8.14. This approach has also been used to provide a unified solution for the thennal rate constant in systems influenced by non-adiabatic effects, i.e. to bridge the adiabatic and non-adiabatic (Golden Rule) limits of such reactions. 

In other words, the ability of the solvent to absorb a quantum of energy h >0 (or its classical equivalent) is determined quite literally by the ability of the solvent to respond to the solute dynamics at a frequency o> = oj(). One can derive this relation quantum mechanically by assuming that the solvent s effect on the solute can be handled perturbatively within Fermi s golden rule (1), but it is actually more general than that. Perhaps it is worth pausing to see how the same basic result appears in a purely classical context. 

By assuming that the dynamic variables follow the same rules as for hydrogen in many-electron atoms, there was the expectation that the periodic table of the elements could be reduced to the Schrodinger solution for hydrogen. Apart from a superficial correlation, which is commonly assumed to vindicate this expectation, it has now been shown that the neglect of general-relativistic curvature of space-time prevents such reduction. Once this defect has been rectified the atomic model will be used to investigate commensurability in the self-similar solar system. 

Equation 3.4 is a particular case of a more general rule the only possible (that is, observable) values for a dynamic variable a whose associated operator is A are the solutions of the equation... 

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