Some properties of WKB series

We investigate some properties of the WKB series for arbitrary analytic potentials and then specifically for potentials $x^N$ ($N$ even), where more explicit formulae for the WKB terms are derived. Our main new results are: (i) We find the explicit functional form for the general WKB terms $\sigma_k'$, where one has only to solve a general recursion relation for the rational coefficients. (ii) We give a systematic algorithm for a dramatic simplification of the integrated WKB terms $\oint \sigma_k'dx$ that enter the energy eigenvalue equation. (iii) We derive almost explicit formulae for the WKB terms for the energy eigenvalues of the homogeneous power law potentials $V(x) = x^N$, where $N$ is even. In particular, we obtain effective algorithms to compute and reduce the terms of these series.Comment: 18 pages, submitted to Journal of Physics A: Mathematical and Genera

DIRAC: The Distributed MC Production and Analysis for LHCb

DIRAC is the LHCb distributed computing grid infrastructure for MC production and analysis. Its architecture is based on a set of distributed collaborating services. The service decomposition broadly follows the CERN/ARDA-RTAG proposal, which can eventually make possible the interchange of the EGEE/gLite and DIRAC components. In this paper we give an overview of the DIRAC architecture, as well as the main design choices in its implementation. The light nature and modular design of the DIRAC components allows its functionality to be easily extended to include new computing and storage elements or to handle new types of tasks. The DIRAC system already uses different types of computing resources - from single PC's to a variety of batch systems and to the Grid environment. In particular, the DIRAC interface to the LCG2 grid will be presented