Generalized ladder operators for shape-invariant potentials

A general form for ladder operators is used to construct a method to solve bound-state Schrödinger equations. The characteristics of supersymmetry and shape invariance of the system are the start point of the approach. To show the elegance and the utility of the method we use it to obtain energy spectra and eigenfunctions for the one-dimensional harmonic oscillator and Morse potentials and for the radial harmonic oscillator and Coulomb potentials.

The Morse oscillator generalised from supersymmetry

Using the factorisation method in supersymmetric quantum mechanics the author determines new potentials from the Morse oscillator. This method is applied although the ladder operators are not used.

Sparse 1D discrete Dirac operators I: Quantum transport

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dynamic Morse decompositions for semigroups of homeomorphisms and control systems

In this paper, we introduce the concept of dynamic Morse decomposition for an action of a semigroup of homeomorphisms. Conley has shown in [5, Sec. 7] that the concepts of Morse decomposition and dynamic Morse decompositions are equivalent for flows in metric spaces. Here, we show that a Morse decomposition for an action of a semigroup of homeomorphisms of a compact topological space is a dynamic Morse decomposition. We also define Morse decompositions and dynamic Morse decompositions for control systems on manifolds. Under certain condition, we show that the concept of dynamic Morse decomposition for control system is equivalent to the concept of Morse decomposition.

Sparse one-dimensional discrete Dirac operators II: Spectral properties

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Exact closed-form solutions of the Dirac equation for a class of effective Morse potentials

Exact bounded solutions for a fermion subject to exponential scalar potential in 1 + 1 dimensions are found in closed form. We discuss the existence of zero modes which are related to the ultrarelativistic limit of the Dirac equation and are responsible for the induction of a fractional fermion number on the vacuum.

Cauchy-Stieltjes Integral on Time Scales in Banach Spaces and Hysteresis Operators

The play operator has a fundamental importance in the theory of hysteresis. It was studied in various settings as shown by P. Krejci and Ph. Laurencot in 2002. In that work it was considered the Young integral in the frame of Hilbert spaces. Here we study the play in the frame of the regulated functions (that is: the ones having only discontinuities of the first kind) on a general time scale T (that is: with T being a nonempty closed set of real numbers) with values in a Banach space. We will be showing that the dual space in this case will be defined as the space of operators of bounded semivariation if we consider as the bilinearity pairing the Cauchy-Stieltjes integral on time scales.

Evaluation of Torque Maintenance of Abutment and Cylinder Screws With Morse Taper Implants

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Solutions of the Fokker-Planck equation for a Morse isospectral potential

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A new type of confinement for the Morse potential

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Solução analítica do potencial de Morse em mecânica clássica

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Comparative Strain Gauge Analysis of External and Internal Hexagon, Morse Taper, and Influence of Straight and Offset Implant Configuration

Purpose: The present study was designed to analyze strain distributions caused by varying the fixture-abutment design and fixture alignment.Materials and Methods: Three implants of external, internal hexagon, and Morse taper were embedded in the center of each polyurethane block in straight placement and offset placement. Four strain gauges (SGs) were bonded on the surface of polyurethane block, which was designated SG1 placed mesially adjacent to implant A, SG2 and SG3 were placed mesially and distally adjacent to the implant B and SG4 was placed distally adjacent to the implant C. The 30 superstructures' occlusal screws were tightened onto the Microunit abutments with a torque of 10 N cm using the manufacturers' manual torque-controlling device.Results: There were statistically significant differences in prosthetic connection (P value = 0.0074 < 0.5). There were no statistically significant differences in placement configuration/alignment (P value = 0.7812 > 0.5).Conclusion: The results showed fundamental differences in both conditions. There was no evidence that there was any advantage to offset implant placement in reducing the strain around implants. The results also revealed that the internal hexagon and Morse taper joints did not reduce the microstrain around implants. (Implant Dent 2011; 20:e24-e32)

Mapping the Wigner distribution function of the Morse oscillator onto a semiclassical distribution function

The mapping of the Wigner distribution function (WDF) for a given bound state onto a semiclassical distribution function (SDF) satisfying the Liouville equation introduced previously by us is applied to the ground state of the Morse oscillator. The purpose of the present work is to obtain values of the potential parameters represented by the number of levels in the case of the Morse oscillator, for which the SDF becomes a faithful approximation of the corresponding WDF. We find that for a Morse oscillator with one level only, the agreement between the WDF and the mapped SDF is very poor but for a Morse oscillator of ten levels it becomes satisfactory. We also discuss the limit h --> 0 for fixed potential parameters.

Multitrace operators and the generalized AdS/CFT prescription

We show that multitrace interactions can be consistently incorporated into an extended AdS conformal field theory (CFT) prescription involving the inclusion of generalized boundary conditions and a modified Legendre transform prescription. We find new and consistent results by considering a self-contained formulation which relates the quantization of the bulk theory to the AdS/CFT correspondence and the perturbation at the boundary by double-trace interactions. We show that there exist particular double-trace perturbations for which irregular modes are allowed to propagate as well as the regular ones. We perform a detailed analysis of many different possible situations, for both minimally and nonminimally coupled cases. In all situations, we make use of a new constraint which is found by requiring consistency. In the particular nonminimally coupled case, the natural extension of the Gibbons-Hawking surface term is generated.

Superstring vertex operators in an AdS(5) x S-5 background

A quantizable action has recently been proposed for the superstring in an AdS(5) x S-5 background with Ramond-Ramond flux. In this paper we construct physical vertex operators corresponding to on-shell fluctuations around the AdS(5) x S-5 background. The structure of these AdS(5) x S-5 vertex operators closely resembles the structure of the massless vertex operators in a flat background. (C) 2001 Elsevier B.V. B.V. All rights reserved.