State spatial attributes

By examining the spatial eharaeter of the wavefiinetions, it is possible to attribute atomie eharaeteristies to the density of states speetnun. For example, the lowest states, 8 to 12 eV below the top of the valenee band, are s-like and arise from the atomie 3s states. From 4 to 6 eV below the top of the valenee band are states that are also s-like, but ehange eharaeter very rapidly toward the valenee band maximum. The states residing within 4 eV of the top of the valenee band are p and arise from the 3p states. 

The selective flux maximization from the FOIST scheme shown in Fig. 2 is achieved by altering the spatial profile of the initial state to be subjected to the photolysis pulse and since changes in flux are due to the flow of probability density, it is useful to examine the attributes of the probability density profiles from the field optimized initial states. 

In the studies that attribute the boundary friction to confined liquid, on the other hand, the interests are mostly in understanding the role of the spatial arrangement of lubricant molecules, e.g., the molecular ordering and transitions among solid, liquid, and amorphous states. It has been proposed in the models of confined liquid, for example, that a periodic phase transition of lubricant between frozen and melting states, which can be detected in the process of sliding, is responsible for the occurrence of the stick-slip motions, but this model is unable to explain how the chemical natures of lubricant molecules would change the performance of boundary lubrication. 

The relatively high activities of these catalysts can in most cases be attributed to the high dispersions of the active species. These are normally incorporated as cations via an ion-exchange process and thus remain bound onto the extensive inner surface of the zeolites by electrostatic forces. The selectivities observed, for example, in oligomerization reactions where, in general, dimers are formed in preference to higher oligomers, may be a direct consequence of the spatial limitations imposed on transition-state complexes within the small zeolite cavities. 

The origin of the temperature-independent solid state broadening, 0.4 eV A <0.6 eV we attributed to spatial variations in the electronic contributions to the intramolecular relaxation energies in the vicinity of the surface (18, 19, 22). Similar widths (to 0.6 eV) have been observed in a variety of other contexts, including condensed thin films of and CO molecules ( ) and the sub-monolayer adsorption of these molecules on metal surfaces (29). Interatomic Auger and electron- hole shakeup processes have been proposed, but found to be too small to account for the observed widths in these cases (28, 48). On... 

Based on these results, the enhanced photoconductivity above 3 eV was attributed to ultrafast interchain charge transfer following photoexcitation into the higher lying excited states [218]. The more delocalized character of the higher excited states (with higher probability of spatial separation between the electron and hole than in the IBu state) was identified as being of principal importance [218]. 

It is noted that the complete Schrodinger equation is a second-order differential equation in the spatial coordinates and a first-order differential equation in the variable time. Therefore, it is not rigorously a wave equation (which would require a second derivative with respect to time). On the other hand, the variable time does not enter the equation as an observable but as a parameter to which well-defined values are attributed. Thus, there are no commutation relations involving a time operator. Nevertheless, it is possible to establish an indeterminacy relation involving energy and time, similar to those previously found for position and momentum. If At is the lifetime of a given state of the system, there will be an indeterminacy in the energy of such a state ... 

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