in this paper, one of the numerical solution method of one- particle, one dimensional timeindependentschrodinger equation are presented that allows one to obtain accurate bound state eigenvalues and functions for an arbitrary potential energy function v(x).for each case, we draw eigen functions versus the related reduced variable for the correspondingenergies. the paper ended with a comparison ...

In this paper, we used quantum chemical approach to shed light on the catalytic mechanism of γ-carbonic anhydrase (γ-CA) to convert carbon dioxide to bicarbonate ion. Density functional theory (DFT) using B3LYP and UB3LYP functional and three split-valance including 6-31G*, 6-311G** and 6-311++G** basis sets were used to calculate the details of electronic structure and electronic energy of act...

Centrifugal-like potentials V (r) ∼ G/r 2 + O(1) may be regularized by a small shift r = x − i ε of the real axis. This enables us to study the (real) energy levels in the potentials V (r) = r 10 + a r 8 + b r 6 + c r 4 + d r 2 + G/r 2. We show that for certain couplings the exact and elementary N−plets of bound states may be constructed at any predetermined N.

A recently discovered relation between 4D and 5D black holes is used to derive exact (weighted) BPS black hole degeneracies for 4D N = 8 string theory from the exactly known 5D degeneracies. A direct 4D microscopic derivation in terms of weighted 4D D-brane bound state degeneracies is sketched and found to agree.

In this paper the problem of the gauge in a bound state calculation is discussed. In particular, in order to verify the gauge invariance in the energy levels expansion, some set of gauge invariant contributions are given. Talk given at the NATO-ASI, Electron Theory and Quantum Electrodynamics, Edirne 8-16 September 1994 E-mail: [email protected]

By using an ansatz for the eigenfunction, we have obtained the exact analytical solutions of the radial Schrödinger equation for the pseudoharmonic and Kratzer potentials in two dimensions. The energy levels of all the bound states are easily calculated from this eigenfunction ansatz. The normalized wavefunctions are also obtained.

Neutrino reaction cross-sections, (ν µ , µ −), (ν e , e −), µ-capture and photoab-sorption rates on 12 C are computed within a large-basis shell-model framework , which included excitations up to 4¯ hω. When ground-state correlations are included with an open p-shell the predictions of the calculations are in reasonable agreement with most of the experimental results for these reactions. Woods-...