Shape invariant hypergeometric type operators with application to quantum mechanics

A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape invariant operators. These operators can be analysed together and the mathematical formalism we use can be extended in order to define other shape invariant operators. All the considered shape invariant operators are directly related to Schrodinger type equations.Comment: More applications available at http://fpcm5.fizica.unibuc.ro/~ncotfa

Mapping of shape invariant potentials by the point canonical transformation

In this paper by using the method of point canonical transformation we find that the Coulomb and Kratzer potentials can be mapped to the Morse potential. Then we show that the P\"{o}schl-Teller potential type I belongs to the same subclass of shape invariant potentials as Hulth\'{e}n potential. Also we show that the shape-invariant algebra for Coulomb, Kratzer, and Morse potentials is SU(1,1), while the shape-invariant algebra for P\"{o}schl-Teller type I and Hulth\'{e}n is SU(2)

Algebraic Approach to Shape Invariance

The integrability condition called shape invariance is shown to have an underlying algebraic structure and the associated Lie algebras are identified. These shape-invariance algebras transform the parameters of the potentials such as strength and range. Shape-invariance algebras, in general, are shown to be infinite-dimensional. The conditions under which they become finite-dimensional are explored.Comment: Submitted to Physical Review A. Latex file, 9 pages. Manuscript is also available at http://nucth.physics.wisc.edu/preprints

Charged particle production in the Pb+Pb system at 158 GeV/c per nucleon

Charged particle multiplicities from high multiplicity central interactions of 158 GeV/nucleon Pb ions with Pb target nuclei have been measured in the central and far forward projectile spectator regions using emulsion chambers. Multiplicities are significantly lower than predicted by Monte Carlo simulations. We examine the shape of the pseudorapidity distribution and its dependence on centrality in detail.Comment: 17 pages text plus 12 figures in postscript 12/23/99 -- Add TeX version of sourc

Dirichlet sigma models and mean curvature flow

The mean curvature flow describes the parabolic deformation of embedded branes in Riemannian geometry driven by their extrinsic mean curvature vector, which is typically associated to surface tension forces. It is the gradient flow of the area functional, and, as such, it is naturally identified with the boundary renormalization group equation of Dirichlet sigma models away from conformality, to lowest order in perturbation theory. D-branes appear as fixed points of this flow having conformally invariant boundary conditions. Simple running solutions include the paper-clip and the hair-pin (or grim-reaper) models on the plane, as well as scaling solutions associated to rational (p, q) closed curves and the decay of two intersecting lines. Stability analysis is performed in several cases while searching for transitions among different brane configurations. The combination of Ricci with the mean curvature flow is examined in detail together with several explicit examples of deforming curves on curved backgrounds. Some general aspects of the mean curvature flow in higher dimensional ambient spaces are also discussed and obtain consistent truncations to lower dimensional systems. Selected physical applications are mentioned in the text, including tachyon condensation in open string theory and the resistive diffusion of force-free fields in magneto-hydrodynamics.Comment: 77 pages, 21 figure

The Amsterdam-Granada Light Scattering Database

The Amsterdam Light Scattering Database proved to be a very successful way of promoting the use of the data obtained with the Amsterdam Light Scattering apparatus at optical wavelengths. Many different research groups around the world made use of the experimental data. After the closing down of the Dutch scattering apparatus, a modernized and improved descendant, the IAA Cosmic Dust Laboratory (CoDuLab), has been constructed at the Instituto de Astrofísica de Andalucía (IAA) in Granada, Spain. The first results of this instrument for water droplets and for two samples of clay particles have been published. We would now like to make these data also available to the community in digital form by introducing a new light scattering database, the Amsterdam-Granada Light Scattering Database (www.iaa.es/scattering). By combining the data from the two instruments in one database we ensure the continued availability of the old data, and we prevent fragmentation of important data over different databases. In this paper we present the Amsterdam-Granada Light Scattering Database