With special attention to the role of information theory in physical sciences we present analytical results for the coordinate- and momentum-space Fisher information of some important one-dimensional quantum systems which differ in spacing of their energy levels. The studies envisaged allow us to relate the coordinate-space information (
) with the familiar energy levels of the quantum system. The corresponding momentum-space information (
) does not obey such a simple relationship with the energy spectrum. Our results for the product (
) depend quadratically on the principal quantum number n and satisfy an appropriate uncertainty relation derived by Dehesa et al (2007 J. Phys. A: Math. Theor. 40 1845)
We make use of a Hylleraas-type wave function to derive an exact analytical model to quantify correlation in two-electron atomic/ionic systems and subsequently employ it to examine the role of inter-electronic repulsion in affecting (i) the bare (uncorrelated) single-particle position-and momentum-space charge distributions and (ii) corresponding Shannon's information entropies. The results presented for the first five members in the helium iso-electronic sequence, on the one hand, correctly demonstrate the effect of correlation on bare charge distributions and, on the other hand, lead us to some important results for the correlated and uncorrelated values of the entropies. These include the limiting behavior of the correlated entropy sum (sum of position-and momentum-space entropies) and geometrical realization for the variation of information entropies as a function of Z. We suggest that, rather than the entropy sum, individual entropies should be regarded as better candidates for the measure of correlation.
Present paper discusses the behaviour of transfer free energy of some amino acids from water to aqueous solution of Ethanol, 2-PrOH ad t-BuOH at different compositions. Dissection of transfer free energy into cavity term, interaction term and electrical term reveals that cavity forming free energy of transfer DG t 0 (Cav.) plays an important role in dictating actual interaction of amino acids in these mixed solvents. Cavity forming free energy of transfer has been estimated by using Scaled Particle Theory (SPT).
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