Title of Talk

Scaling properties of net information measures and statistical complexity for bound states of spherical model potentials

 

Abstract

The quantum mechanical Heisenberg uncertainty product is expressed in terms of the standard deviations involving quantum expectation values. The net information theoretical uncertainty-like measures, derived from the measures due to Shannon, Fisher, and others and computed in the position and momentum space provide interesting representations in terms of electron densities. Using the common dimensional properties of the uncertainty measures in general, we present their scaling characteristics in terms of the parameters of several standard non-relativistic spherical model potentials, V (r) which generate the electron densities from the wave functions. Significance of the scaling properties with the illustrative numerical tests of the scaling behavior will be presented. A similar study involving the statistical complexity measure corresponding to several of these model potentials will also be discussed. A new measure of the relative statistical complexity will be introduced and its applications to the electronic structure of atoms will be presented.

 

References:

1. W Heisenberg, Z. Phys. 43 (1927) 172

2. K.D. Sen, J. Katriel, J. Chem. Phys. 125 (2006) 074117

3. S.H. Patil, K.D. Sen, Phys. Lett. A 362 (2007) 109

4. K.D. Sen, Statistical Complexity: Applications in Electronic Structure, Springer U.K. (2011)

5. K.D. Sen, S.H. Patil, Concepts and Methods in Modern Theoretical Chemistry Eds. CRC Press Taylor and Francis Group (2013) 441

Kalidas Sen, Professor

 

School of Chemistry, University of Hyderabad, Hyderabad-500 046, INDIA

e-mail: sensc@uohyd.ernet.in

Profile. Kalidas Sen (PhD, IIT-Kanpur) F.A.Sc., F.N.A. joined University of Hyderabad in 1977 where he continues to teach as a professor of chemistry. His research efforts in electronic structure theory have led to the publication of 8 monographs and 190 research papers in prestigious international journals. His most recent monograph entitled "Statistical Complexity: Applications in Electronic Structure" has been published by Springer, UK in October 2011. A recipient of Humboldt, Commonwealth, Fulbright, and NSERC Canada Research Fellowship, he has been recently awarded the DAAD Research Professorship, Indo-US Professor of Physics of the American Physical Society, Visiting Fellowship of the Office of Naval Research Laboratory, Washington, and the J.C. Bose National Fellowship.

 

Selected Publications

1. ‘ELECTRONEGATIVITY’ Structure and Bonding, Vol. 66 (1987), Edited by K.D. Sen and C.K. Jorgensen.(Springer-Verlag,Heidelberg)

2. ‘CHEMICAL HARDNESS’, Structure and Bonding, Ed. Sen, K.D. 1993, Vol.80. .(Springer-Verlag,Heidelberg)

3. ‘MOLECULAR SIMILARITY’, Topics in Current Chemistry, Ed. Sen, K.D. 1995, Vol.173-174 .(Springer-Verlag, Heidelberg)

4.  ‘ELECTROSTATIC POTENTIAL FOR ATOMS AND MOLECULES’, Topics in Computational Chemistry, Ed. Sen, K.D. & Murray, J. 1996, Elsevier, Amsterdam

5. REVIEWS IN MODERN QUANTUM CHEMISTRY: A CELEBRATION OF THE CONTRIBUTIONS OF ROBERT G PARR, 2002, World Scientific Publishing Company, Singapore (Vol I and II, 1804 pages total)