On a Generalized Oscillator System: Interbasis Expansions

This article deals with a nonrelativistic quantum mechanical study of a dynamical system which generalizes the isotropic harmonic oscillator system in three dimensions. The problem of interbasis expansions of the wavefunctions is completely solved. A connection between the generalized oscillator system (projected on the z-line) and the Morse system (in one dimension) is discussed.Comment: 23 pages, Latex File, to be published in International Journal of Quantum Chemistr

On a Generalized Oscillator: Invariance Algebra and Interbasis Expansions

This article deals with a quantum-mechanical system which generalizes the ordinary isotropic harmonic oscillator system. We give the coefficients connecting the polar and Cartesian bases for D=2 and the coefficients connecting the Cartesian and cylindrical bases as well as the cylindrical and spherical bases for D=3. These interbasis expansion coefficients are found to be analytic continuations to real values of their arguments of the Clebsch-Gordan coefficients for the group SU(2). For D=2, the superintegrable character for the generalized oscillator system is investigated from the points of view of a quadratic invariance algebra.Comment: 13 pages, Latex file. Submitted for publication to Yadernaya Fizik

The Cosmic Microwave Background and Inflation Parameters

We review the currrent cosmic parameter determinations of relevance to inflation using the WMAP-1year, Boomerang, CBI, Acbar and other CMB data. The basic steps in the pipelines which determine the bandpowers from the raw data from which these estimations are made are summarized. We forecast how the precision is likely to improve with more years of WMAP in combination with future ground-based experiments and with Planck. We address whether the current data indicates strong breaking from uniform acceleration through the relatively small region of the inflaton potential that the CMB probes, manifest in the much-discussed running spectral index or in even more radical braking/breaking scenarios. Although some weak ``anomalies'' appear in the current data, the statistical case is not there. However increased precision, at the high multipole end and with polarization measurements, will significantly curtail current freedom.Comment: 24 pages, 10 figures, 2 tables, Int. J. Theor. Phys. 2004, ed. E. Verdaguer, "Peyresq Physics 8", "The Early Universe: Confronting theory with observations" (June 21-27, 2003

Superintegrability and associated polynomial solutions: Euclidean space and the sphere in two dimensions

In this work we examine the basis functions for those classical and quantum mechanical systems in two dimensions which admit separation of variables in at least two coordinate systems. We do this for the corresponding systems defined in Euclidean space and on the two-dimensional sphere. We present all of these cases from a unified point of view. In particular, all of the special functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial bases for each of the nonsubgroup bases, not just the subgroup Cartesian and polar coordinate cases, and the details of the structure of the quadratic algebras. We also study the polynomial eigenfunctions in elliptic coordinates of the n-dimensional isotropic quantum oscillator