440 research outputs found
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
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