25 research outputs found

    The orthogonality of q-classical polynomials of the Hahn class: A geometrical approach

    Get PDF
    The idea of this review article is to discuss in a unified way the orthogonality of all positive definite polynomial solutions of the qq-hypergeometric difference equation on the qq-linear lattice by means of a qualitative analysis of the qq-Pearson equation. Therefore, our method differs from the standard ones which are based on the Favard theorem, the three-term recurrence relation and the difference equation of hypergeometric type. Our approach enables us to extend the orthogonality relations for some well-known qq-polynomials of the Hahn class to a larger set of their parameters. A short version of this paper appeared in SIGMA 8 (2012), 042, 30 pages http://dx.doi.org/10.3842/SIGMA.2012.042.Comment: A short version of this paper appeared in SIGMA 8 (2012), 042, 30 pages http://dx.doi.org/10.3842/SIGMA.2012.04

    High-Precision Numerical Determination of Eigenvalues for a Double-Well Potential Related to the Zinn-Justin Conjecture

    Full text link
    A numerical method of high precision is used to calculate the energy eigenvalues and eigenfunctions for a symmetric double-well potential. The method is based on enclosing the system within two infinite walls with a large but finite separation and developing a power series solution for the Schro¨\ddot{o}dinger equation. The obtained numerical results are compared with those obtained on the basis of the Zinn-Justin conjecture and found to be in an excellent agreement.Comment: Substantial changes including the title and the content of the paper 8 pages, 2 figures, 3 table

    Part of the D - dimensional Spiked harmonic oscillator spectra

    Full text link
    The pseudoperturbative shifted - l expansion technique PSLET [5,20] is generalized for states with arbitrary number of nodal zeros. Interdimensional degeneracies, emerging from the isomorphism between angular momentum and dimensionality of the central force Schrodinger equation, are used to construct part of the D - dimensional spiked harmonic oscillator bound - states. PSLET results are found to compare excellenly with those from direct numerical integration and generalized variational methods [1,2].Comment: Latex file, 20 pages, to appear in J. Phys. A: Math. & Ge

    Short-range oscillators in power-series picture

    Get PDF
    A class of short-range potentials on the line is considered as an asymptotically vanishing phenomenological alternative to the popular confining polynomials. We propose a method which parallels the analytic Hill-Taylor description of anharmonic oscillators and represents all our Jost solutions non-numerically, in terms of certain infinite hypergeometric-like series. In this way the well known solvable Rosen-Morse and scarf models are generalized.Comment: 23 pages, latex, submitted to J. Phys. A: Math. Ge

    The power of perturbation theory

    Get PDF
    We study quantum mechanical systems with a discrete spectrum. We show that the asymptotic series associated to certain paths of steepest-descent (Lefschetz thimbles) are Borel resummable to the full result. Using a geometrical approach based on the PicardLefschetz theory we characterize the conditions under which perturbative expansions lead to exact results. Even when such conditions are not met, we explain how to define a different perturbative expansion that reproduces the full answer without the need of transseries, i.e. non-perturbative effects, such as real (or complex) instantons. Applications to several quantum mechanical systems are presented

    Waste Generation, Incineration and Landfill Diversion: De-Coupling Trends, Socio-Economic Drivers and Policy Effectiveness in the EU

    Full text link
    corecore