Nonperturbative approach to potentials in impenetrable boxes based on quasi-exact solvability

In this work we develop an approach to obtain analytical expressions for potentials in an impenetrable box. In this kind of system the expression has the advantage of being valid for arbitrary values of the box length, and respect the correct quantum limits. The similarity of this kind of problem with the quasi exactly solvable potentials is explored in order to accomplish our goals. Problems related to the break of symmetries and simultaneous eigenfunctions of commuting operators are discussed.

Structure of potentials with N higgs doublets

Extensions of the standard model with N Higgs doublets are simple extensions presenting a rich mathematical structure. An underlying Minkowski structure emerges from the study of both variable space and parameter space. The former can be completely parametrized in terms of two future lightlike Minkowski vectors with spatial parts forming an angle whose cosine is -(N-1)(-1). For the parameter space, the Minkowski parametrization enables one to impose sufficient conditions for bounded below potentials, characterize certain classes of local minima, and distinguish charge breaking vacua from neutral vacua. A particular class of neutral minima presents a degenerate mass spectrum for the physical charged Higgs bosons.

Electrochemical stability of anodic titanium oxide films grown at potentials higher than 3 V in a simulated physiological solution

The cathodic behaviour of oxides formed on titanium electrodes in physiological solutions at potentials between 3 and 5 V (vs. SCE) was studied by cyclic voltammetry. In case of anodic polarization at potentials higher than 3 V (vs. SCE), a cathodic peak at similar to 0.4 V (vs. SCE) appears in the cathodic scan, which could be due to the reduction of unstable peroxides. The results show that this peak depends on the anodic potential and the oxidation time. This behaviour supposedly is due to the formation of unstable titanium peroxides like TiO3 during anodization. Based on repetitive oxidation-reduction processes can be concluded that the created amount of TiO3 inside of the TiO2 surface layer seems to be constant. (c) 2006 Elsevier Ltd. All rights reserved.

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.

Synthesis, structure and redox properties of an unexpected trinuclear copper(II) complex with aspartame: [Cu(apm)(2)Cu(mu-N,O : O '-apm)(2)(H2O)Cu(apm)(2)(H2O)]center dot 5H(2)O

Structural, magnetic and spectroscopic data of a new trinuclear copper(II) complex with the ligand aspartame (apm) are described. [Cu(apm)(2)CU(mu-N,O:O'-apm)(2)(H2O)Cu(apm)(2)(H2O)]-5H(2)O crystallizes in the triclinic system, space group P1 (#1) with a = 7.3300(1) angstrom, b = 15.6840(1) angstrom, c = 21.5280(1) angstrom, alpha = 93.02(1)degrees, beta = 93.21 (1)degrees, gamma = 92.66(1)degrees and Z = 1. Aspartame coordinates to Cu(II) through the carboxylate and beta-amino groups. The carboxylate groups of the two central ligands act as bidentate bridges in a syn-anti conformation while the carboxylate groups of the four peripheral ligands are monodentate in a syn conformation. The central copper ion is in a distorted square pyramidal geometry with the apical position being occupied by one oxygen atom of the water molecule. The two terminal copper(II) atoms are coordinated to the ligands in the same position but their coordination sphere differs from each other due to the fact that one copper atom has a water molecule in an apical position leading to an octahedral coordination sphere while the other copper atom is exclusively coordinated to aspartame ligands forming a distorted square pyramidal coordination sphere. Thermal analysis is consistent with the X-ray structure. EPR spectra and CV curves indicate a rupture of the trinuclear framework when this complex is dissolved in ethanol or DMF, forming a mononuclear species, with a tetragonal structure. (c) 2005 Elsevier B.V. All rights reserved.

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.

Kinetics and mechanism of the induced redox reaction of [Ni(cyclam)](2+) promoted by SO5 center dot-

Oxidation of [Ni(cyclam)](2+), cyclam = 1,4,8,11-tetraazacyclotetradecane, accelerated by sulfur dioxide, was studied spectrophotometrically by following the formation of [Ni(cyclam)](3+) under the conditions: [Ni(cyclam)](2+) = 6.0 x 10(-3) M; initial [Ni(cyclam)](3+) = 8.0 x 10(-6) M; [cyclam] = 6.0 x 10(-3) M; [SO2] = (1.0-5.0) x 10(-4) M and 1.0 M perchloric acid in oxygen saturated solutions at 25.0 degrees C and ionic strength = 1.0 M. The oxidation reaction exhibits autocatalytic behavior in which the induction period depends on the initial Ni(III) concentration. A kinetic study of the reduction of Ni(III) by SO2 under anaerobic conditions, and the oxidation of Ni(II), showed that the rate-determining step involves reduction of Ni(III) by SO2 to produce the SO3.- radical, which rapidly reacts with dissolved oxygen to produce SO5.- and rapidly oxidizes Ni(II). The results clearly show a redox cycling process which depends on the balance of SO2 and oxygen concentrations in solution.

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.

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.

INFLUENCE OF DIABETES-MELLITUS ON THE GLUTATHIONE REDOX SYSTEM OF HUMAN RED-BLOOD-CELLS

Several components of the erythrocyte-dependent glutathione redox system (reduced glutathione, GSH; oxidized glutathione, GSSG; glutathione peroxidase, GSH-Px; glutathione reductase, GSH-Red) were determined in patients with types I and II diabetes mellitus (DM). All groups studied were male subjects: G1, 20 young healthy individuals (aged 23.7 +/- 4.2 years); G2, 15 young insulin-treated type I DM patients; G3, 20 older insulin-treated type II DM patients; 04, 21 older oral hypoglycemic agent-treated type II DM patients; G5, 28 aged healthy individuals (aged 68.9 +/- 11.5 years). There were no differences between G1 and G2, G3 or G4 regarding erythrocyte GSH, GSSG, and GSH-Red (without FAD) levels. GSH-Px activity was significantly lower in G2 when compared to G1 (15.2 +/- 4.9 vs 20.6 +/- 6.6 IU/g Hb). The GSH-Red and GSH-Px activities and GSH levels were significantly higher in 03 (4.6 +/- 1.7 IU/g Hb, 20.2 +/- 8.7 IU/g Hb and 3.5 +/- 1.3-mu-M/g Hb) and G4 (5.0 +/- 2.2 IU/g Hb, 16.9 +/- 6.1 IU/g Hb and 5.0 +/- 2.3-mu-M/g Hb) when compared to G5 (3.4 +/- 0.9 IU/g Hb, 12.0 +/- 3.6 IU/g Hb and 2.3 +/- 0.9-mu-M/g Hb). The findings suggest that treatment of DM can stimulate the redox activity of red blood cells in aged subjects.

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.

Thermogravimetric and UV-vis spectroscopic studies of chromium redox reactions in rutile pigments

In this study undoped and Cr, Sb or Mo doped TiO(2) were synthesized by polymeric precursor method and characterized by X-ray diffraction, UV-VIS spectroscopy, infrared spectroscopy and thermogravimetry (TG). The TG curves showed a continuous mass loss assigned to the hydroxyl elimination and Cr(6+) reduction. Doped TiO(2) samples showed a higher mass loss assigned to water and gas elimination at lower temperatures. In these doped materials a decrease in the anatase-rutile phase transition temperature was observed. After calcination at 1,000 A degrees C, rutile was obtained as a single phase material without the presence of Cr(6+).