Abstract: The most fundamental equation of Theoretical Chemistry and of Atomic Physics is the Schroedinger equation for a hydrogen like system. Its solution can be found in any standard textbook on Atomic Physics, Quantum Chemistry and so on. A similar equation which is somewhat more complicated is the Schroedinger equation for a particle bound in what is known in the literature as screened Coulomb potential. The screening function that will be discussed is one which is solely dependent on the radial variable r and is known in the literature as the Yukawa potential. This potential arises naturally as the position space version of the solution of the Klein-Gordon equation for a static meson field. It was the deuteron problem which inspired the first solutions to the corresponding eigenvalue equation. It is commonly known in plasma physics as the “Debye-Hueckel” potential and represents the effect of the plasma sea on localized two-particle interactions. The Debye-Hueckel potential also approximates the Thomas-Fermi potential in the calculation of the energy levels of the impurity centers in doped semiconductors. Together with the Hulten and the exponential potentials the Yukawa potential plays an important role as a good test case in potential scattering studies also. In quantum chemistry the effect of the core electrons on the valence electrons can be modeled by means of a linear combination of Yukawa or similar potentials. Various approaches have been made to attempt to solve the eigenvalue problem associated to the corresponding Schroedinger equation having Yukawa or similar screened coulomb potentials. Quite a few of these use perturbational and variational techniques. There were also group theoretical approaches. Direct numerical integration of the corresponding Schroedinger equation were also employed and quite succesfully so. Regge trajectories were determined via this means or by utilizing continued fractions. There are of course plenty of other works related to Yukawa potential. The method that will be discussed during the talk is also based on variational treatment of the radial Schroedinger equation with Yukawa potential. It employs a Laguerre basis set extended by an extra function. A parameter used in this extra function and its relation with the energy of the system results in the utilization of an auto-coherent (or self-consistent) scheme. The proposed method does not only give energy values for the ground and the first few excited states consistently up to thirty digits but also gives threshold screening parameter values accurate to 15-20 decimal points.

Brief Biography of the Speaker:
N. A. BAYKARA was born in Istanbul,Turkey on 29th July 1948. He received a B.Sc. degree in Chemistry from Bosphorous University in 1972. He obtained his PhD from Salford University, Greater Manchester, Lancashire,U.K. in 1977 with a thesis entitled “Studies in Self Consistent Field Molecular Orbital Theory”, Between the years 1977–1981 and 1985–1990 he worked as a research scientist in the Applied Maths Department of The Scientific Research Council of Turkey. During the years 1981-1985 he did postdoctoral research in the Chemistry Department of Montreal University, Quebec, Canada. Since 1990 he is employed as a Staff member of Marmara University. He is now a Full Professor of Applied Mathematics mainly teaching Numerical Analysis courses and is involved in HDMR research and is a member of Group for Science and Methods of Computing in Informatics Institute of Istanbul Technical University. Other research interests of his for him are “Density Functional Theory” and “Fluctuationlessness Theorem and its Applications” which he is actually involved in. Most recent of his concerns is focused at efficient remainder calculations of Taylor expansion via Fluctuation–Free Integration, and Fluctuation–Free Expectation Value Dynamics.