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125 Elementary Enrollment Rates (%) 100 75 50 25 150 0 1966 275 1970 599 1975 1980 1985 1990 1995 0 1,643 10,000 GDP per Capita ($) 7,500 5,891 Tertiary 2,292 5,000 2,500 10,881 12,500

Let us now calculate the mean quadratic values of the position and of the momentum z|Q 2 |z = q 2 + 1 , 2 z|P 2 |z = p 2 + 1 2

Summary

(327) P 2 + Q 2 that (328)



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The absolutely quantal face of the coherent states reappears here Indeed, the additional term 1 , called symplectic correction or vacuum energy according to 2 the context, has no classical counterpart Finally, from the respective variances of position and momentum, ( Q)2 = z|Q 2 Q 2 |z = z

Figure 11 Education and Wealth: South Korean Enrollment Rates vs Economic Growth, 1966 1995

= ( P )2 ,

$ dpkg --list *lsof*

we infer the saturation of the uncertainty relation or, more properly, Heisenberg inequality: Q P = 1 2 = (329)

This is one of the most important features exhibited by coherent states: their quantal face is the closest possible to its classical counterpart





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driving force for the interaction of nucleophiles with the transuranium cations Water is only one example of a nucleophilic ligand Other nucleophilic ligands present in solution may replace water molecules directly bound to the metal cation to form inner sphere complexes or alternatively, they may displace water molecules only from the outer hydrate shell to form outer sphere complexes Because of the competition between water and other ligands for positions in the inner coordination sphere of the central transuranium atom, it is not surprising that the stability of the complexes formed with a given ligand decreases, in the order M4 MO2 2 M3 MO2 (Note that the strength of complexation does not depend simply on the net cation charge but rather the charge density seen by the anion or ligand as it approaches the metal In the case of MO2 2 , the effective charge is about 3.

From the eigenvalue equation H|n = n + 1 |n for the Hamiltonian of the oscil2 lator, one deduces the time evolution of a coherent state: e iHt |z =e

zn e iHt |n n!

e it z |n n! (330)

3 rather than 2) Although there is some variation within the given cation types, the general order of complexing power of different anions is F NO3 Cl ClO4 for singly charged anions and CO2 2 C2 O4 2 SO4 2 for doubly charged anions The actinide cations are hard acids, that is, their binding to ligands is described in terms of electrostatic interactions, and they prefer to interact with hard bases such as oxygen or uorine rather than softer bases such as nitrogen or sulfur The actinide cations do form complexes with the soft bases but only in nonaqueous solvents As typical hard acids, the stabilities of the actinide complexes are due to favorable entropy effects The enthalpy terms are either endothermic or very weakly exothermic and are of little importance in determining the overall position of the equilibrium in complex formation.

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We thus ascertain the temporal stability of the family {|z , z C} or {|z , z C}

since a quantum state is de ned up to a phase factor There follows the illuminating form of this time evolution in position representation:

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