Quantum mechanics numerical examples expectation

It was mentioned in Section III,A, 1 that, as indicated by the results of quantum mechanical calculations, phenothiazine is an excellent electron donor the numerous examples in the previous subsections dealing with the oxidation of phenothiazines also illustrated the ease with which electrons are lost by the derivatives of this heterocycle. Consequently, phenothiazine charge-transfer complexes with various acceptors are expected. 

It is also interesting to consider the classical/quantal correspondence in the number of energized molecules versus time N(/, E), Eq. (8.22), for a microcanonical ensemble of chaotic trajectories. Because of the above zero-point energy effect and the improper treatment of resonances by chaotic classical trajectories, the classical and quantal I l( , t) are not expected to agree. For example, if the classical motion is sufficiently chaotic so that a microcanonical ensemble is maintained during the decomposition process, the classical N(/, E) will be exponential with a rate constant equal to the classical (not quantal) RRKM value. However, the quantal decay is expected to be statistical state specific, where the random 4i s give rise to statistical fluctuations in the k and a nonexponential N(r, E). This distinction between classical and quantum mechanics for Hamiltonians, with classical f (/, E) which agree with classical RRKM theory, is expected to be evident for numerous systems. 

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