Ladder operators for subtle hidden shape-invariant potentials

Ladder operators can be constructed for all potentials that present the integrability condition known as shape invariance, satisfied by most of the exactly solvable potentials. Using the superalgebra of supersymmetric quantum mechanics, we construct the ladder operators for two exactly solvable potentials that present a subtle hidden shape invariance.

Hamiltonian hierarchy of pseudo-potentials

The general structure of the Hamiltonian hierarchy of the pseudo-Coulomb and pseudo-Harmonic potentials is constructed by the factorization method within the supersymmetric quantum mechanics (SQMS) formalism. The excited states and spectra of eigenfunctions of the potentials are obtained through the generation of the members of the hierarchy. It is shown that the extra centrifugal term added to the Coulomb and Harmonic potentials maintain their exact solvability.

GENERAL POTENTIALS DESCRIBED BY SO(2,1) DYNAMIC ALGEBRA IN PARABOLIC-COORDINATE SYSTEMS

We propose general three-dimensional potentials in rotational and cylindrical parabolic coordinates which are generated by direct products of the SO(2, 1) dynamical group. Then we construct their Green functions algebraically and find their spectra. Particular cases of these potentials which appear in the literature are also briefly discussed.

Barrier penetration for supersymmetric shape-invariant potentials

Exact reflection and transmission coefficients for supersymmetric shape-invariant potentials barriers are calculated by an analytical continuation of the asymptotic wavefunctions obtained via the introduction of new generalized ladder operators. The general form of the wavefunction is obtained by the use of the F(-infinity, +infinity)-matrix formalism of Froman and Froman which is related to the evolution of asymptotic wavefunction coefficients.

GROUND-STATE-ENERGY OF SINGULAR POTENTIALS

It is shown that for singular potentials of the form lambda/r(alpha),the asymptotic form of the wave function both at r --> infinity and r --> 0 plays an important role. Using a wave function having the correct asymptotic behavior for the potential lambda/r(4), it is, shown that it gives the exact ground-state energy for this potential when lambda --> 0, as given earlier by Harrell [Ann. Phys. (NY) 105, 379 (1977)]. For other values of the coupling parameter X, a trial basis;set of wave functions which also satisfy the correct boundary conditions at r --> infinity and r --> 0 are used to find the ground-state energy of the singular potential lambda/r(4) It is shown that the obtained eigenvalues are in excellent agreement with their exact ones for a very large range of lambda values.

Completeness of coherent states associated with self-similar potentials and Ramanujan's integral extension of the beta function

A decomposition of identity is given as a complex integral over the coherent states associated with a class of shape-invariant self-similar potentials. There is a remarkable connection between these coherent states and Ramanujan's integral extension of the beta function.

Properties and one-step synthesis of (2-acetylpyridine)tetraammineruthenium(II), [Ru-II(2-acpy)(NH3)(4)](2+) and tetraammine(2-benzoylpyridine)ruthenium(II), [Ru-II(NH3)(4)(2-bzpy)](2+) Redox potentials, UV-Vis and NMR spectra

A more direct and efficient route to the syntheses of [Ru(NH3)(4)(X-Y)](BF4)(2), where X-Y can be 2-acetylpyridine (2-acpy) or 2-benzoylpyridine (2-bzpy), based on the reactions of [RuCl(NH3)(5)]Cl-2 with these ortho-substituted azines is described. The [Ru(2-acpy)(NH3)(4)](BF4)(2) and [Ru(NH3)(5)(2-bzpy)](BF4)(2) complexes have a molar conductance of 328 and 292 Ohm(-1) cm(2) mol(-1), respectively, corresponding to a 1:2 species in solution. These complexes showed two intense absorption bands around 620-650 and 380 nm, the energies of which are solvent dependent, decreasing with the increase of the Gutman's donor number of the solvent, and were assigned as metal-to-ligand charge transfer (MLCT). The complexes have oxidation potentials (Ru-II/III) of +0.380 V vs. Ag/AgCl (2-acpy) and +0.400 V vs. Ag/AgCl (2-bzpy), and reduction potentials (X-Y0/-) of -1.10 V vs. Ag/AgCl (2-acpy) and -0.950 V vs. Ag/AgCl (2-bzpy) on CF3COOH/NaCF3COO at pH=3.0, scan rate 100 mV s(-1), [Ru]=1.0x10(-3) mol l(-1). Both processes show a coupled chemical reaction. Upon oxidation of the metal center, the MLCT absorption bands are bleached and restored upon subsequent reduction. In order to confirm the structure of the complexes a detailed LH NMR investigation was performed in d(6)-acetone. Further confirmation of the structure was obtained by recording the N-15 NMR spectrum of [Ru(NH3)(4)(2-bzpy)](2+) in d(6)-DMSO using the INEPT pulse sequence improving the sensitivity of N-15 by polarization transfer from the protons to the N-15. The Nuclear Overhauser Effect (NOE) experiments were made qualitatively for [Ru(NH3)(4)(2-acpy)](2+), and showed that H-6 of the pyridine is close to a NH3 proton, which should then be in a cis position, and, hence, confirming that acpy is acting as a bidentate ligand. (C) 1999 Elsevier B.V. Ltd. All rights reserved.

Using an effective surface charge to explain surface potentials of Langmuir monolayers from dialkyldimethylammonium halides with the Gouy-Chapman theory

The use of an effective surface charge density has allowed the Gouy-Chapman (CC) theory to explain surface potential isotherms of Langmuir monolayers of dioctadecyldimethylammonium bromide (DODAB). The effective surface charge density of DODAB monolayer increases with the electronegativity of the counterions in the subphase. The pressure-area isotherms indicate a very condensed monolayer for DODAB spread on an I--containing subphase, which exhibits the lowest surface charge density, whereas the monolayer on a F-containing subphase is extremely expanded owing to the high surface charge density or electrostatic repulsion between headgroups. (C) 2001 Published by Elsevier B.V. B.V.

Changes of microstructure in alpha AgZn during post-deformation annealing after cold-rolling

The annealing processes of deformation-induced defects after cold-rolling to about 30 and 60% thickness reduction were investigated for Ag-21, 23, 28 at% Zn by means of residual electrical resistivity, microhardness, light microscopy and transmission electron microscopy (TEM) Three annealing stages have been detected and consistently interpreted as annealing-out of mainly point defects and their agglomerates (stage I), formation of dislocation cells and recrystallized strain-free grains (stage II) and grain growth (stage III). Further, it is tried to determine the evolution of defect production (point defects and dislocations) during rolling deformation from measured changes of electrical resistivity and microhardness. Copyright (C) 1996 Acta Metallurgica Inc.

Bound states of the Dirac equation for a class of effective quadratic plus inversely quadratic potentials

The Dirac equation is exactly solved for a pseudoscalar linear plus Coulomb-like potential in a two-dimensional world. This sort of potential gives rise to an effective quadratic plus inversely quadratic potential in a Sturm-Liouville problem, regardless the sign of the parameter of the linear potential, in sharp contrast with the Schrodinger case. The generalized Dirac oscillator already analyzed in a previous work is obtained as a particular case. (C) 2004 Elsevier B.V. All rights reserved.

Critical current degradation of Bi-2223 composite tapes induced by cyclic deformation and fatigue-related effects

Application of high temperature superconductor Bi2Sr2Ca2Cu3Ox. (Bi-2223) compound embedded in an Ag matrix requires the knowledge of critical current as a function of mechanical properties. Commercial tapes available in different types have been developed in industrial production scale in which a combination of small diameter filaments, long tape lengths and a ductile matrix results in a conductor with low crack formation and good tolerance against strain. The measurement of critical current and the evaluation of n-index from V-I characteristic curves of Bi-2223/Ag composite tapes subjected to an initial bending strain as a function of number of thermal cycles were done for two types of Bi-2223/Ag composite tapes: with and without steel tape reinforcement. The results showed that tapes with reinforcement presented small critical current degradation as a function of the number of thermal cycles whereas tapes without reinforcement exhibited steadily critical current degradation caused by the propagation of cracks. The n-index followed the same critical current behavior.

BaZrO3 Photoluminescence Property: An Ab Initio Analysis of Structural Deformation and Symmetry Changes

This article reports a theoretical study based on experimental results for barium zirconate, BaZrO3 (BZ) thin films, using periodic mechanic quantum calculations to analyze the symmetry change in a structural order-disorder simulation. Four periodic models were simulated using CRYSTAL98 code to represent the ordered and disordered BZ structures. The results were analyzed in terms of the energy level diagrams and atomic orbital distributions to explain and understand the BZ photoluminescence properties (PL) at room temperature for the disordered structure based on structural deformation and symmetry changes. (C) 2009 Wiley Periodicals, Inc. Int J Quantum Chem 111: 694-701, 2011

Structural deformation monitored by vibrational properties and orbital modeling in (Pb,Sm)TiO3 systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Tensor3D: A computer graphics program to simulate 3D real-time deformation and visualization of geometric bodies

Tensor3D is a geometric modeling program with the capacity to simulate and visualize in real-time the deformation, specified through a tensor matrix and applied to triangulated models representing geological bodies. 3D visualization allows the study of deformational processes that are traditionally conducted in 2D, such as simple and pure shears. Besides geometric objects that are immediately available in the program window, the program can read other models from disk, thus being able to import objects created with different open-source or proprietary programs. A strain ellipsoid and a bounding box are simultaneously shown and instantly deformed with the main object. The principal axes of strain are visualized as well to provide graphical information about the orientation of the tensor's normal components. The deformed models can also be saved, retrieved later and deformed again, in order to study different steps of progressive strain, or to make this data available to other programs. The shape of stress ellipsoids and the corresponding Mohr circles defined by any stress tensor can also be represented. The application was written using the Visualization ToolKit, a powerful scientific visualization library in the public domain. This development choice, allied to the use of the Tcl/Tk programming language, which is independent on the host computational platform, makes the program a useful tool for the study of geometric deformations directly in three dimensions in teaching as well as research activities. (C) 2007 Elsevier Ltd. All rights reserved.