Characterization of the Chandrasekhar correlated two-electron wavefunction using Fisher, Shannon and statistical complexity information measures

The three-parameter two-electron correlated analytic wavefunction of Chandrasekhar, parametrized using three physically meaningful conditions on the electron density, is assessed using several information theory measures, the Fisher information, Shannon entropy, and statistical complexity, and compared to the results for the same measures using hydrogenic and Hartree-Fock (HF) orbitals.

[1]  E. H. Kennard.  Zur Quantenmechanik einfacher Bewegungstypen , 1927 .

[2]  Jaime Sanudo,et al.  Some features of the statistical complexity, Fisher–Shannon information and Bohr-like orbits in the quantum isotropic harmonic oscillator , 2008, 0803.2968.

[3]  Ricardo López-Ruiz,et al.  A Statistical Measure of Complexity , 1995, ArXiv.

[4]  B. Frieden.  Science from Fisher Information , 2004 .

[5]  Rory A. Fisher,et al.  Theory of Statistical Estimation , 1925, Mathematical Proceedings of the Cambridge Philosophical Society.

[6]  M. Grypeos,et al.  The HVT Technique and the "Uncertainty" Relation for Central , 2004, HNPS Advances in Nuclear Physics.

[7]  Charlotte Froese Fischer,et al.  The Hartree-Fock method for atoms: A numerical approach , 1977 .

[8]  Jesús S. Dehesa,et al.  The Fisher information of single-particle systems with a central potential , 2005 .

[9]  I. Bialynicki-Birula,et al.  Uncertainty relations for information entropy in wave mechanics , 1975 .

[10]  S. Chandrasekhar.  Some remarks on the negative hydrogen ion and its absorption coefficient , 1944 .

[11]  S. Dong,et al.  Radial position–momentum uncertainties for the Dirac hydrogen-like atoms , 2006 .

[12]  N. H. March,et al.  Correlated analytic ground-state densities for two-electron atomic ions from Be to Ne , 2007 .

[13]  Ricardo López-Ruiz,et al.  Features of the extension of a statistical measure of complexity to continuous systems. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  L. Green,et al.  Correlation Energies and Angular Components of the Wave Functions of the Ground States ofH−, He i, and Li ii , 1954 .

[15]  Jaime Sanudo,et al.  Statistical complexity and Fisher–Shannon information in the H-atom , 2008, 0803.2859.

[16]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[17]  W. Heisenberg.  Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik , 1927 .

[18]  Claude E. Shannon,et al.  The mathematical theory of communication , 1950 .

[19]  K. Sen.  Shell-confined hydrogen atom. , 2005, The Journal of chemical physics.

[20]  B. Tsapline.  Expectation values in one- and two-electron atomic systems , 1970 .

[21]  C. Kuo.  The uncertainties in radial position and radial momentum of an electron in the non-relativistic hydrogen-like atom , 2005 .

[22]  V. Majerník,et al.  Entropic uncertainty relations for the infinite well , 1997 .

[23]  J. C. Angulo,et al.  Fisher-Shannon analysis of ionization processes and isoelectronic series , 2007 .