Related papers: On Interbasis Expansion for Isotropic Oscillator o…
This article deals with nonrelativistic study of a D-dimensional superintegrable system, which generalizes the ordinary isotropic oscillator system. The coefficients for the expansion between the hyperspherical and Cartesian bases…
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…
The Schr\"odinger equation is thoroughly analysed for the isotropic oscillator in the three-dimensional space of constant positive curvature in the spherical and cylindrical systems of coordinates. The expansion coefficients between the…
This article deals with a nonrelativistic quantum mechanical study of a charge-dyon system with the SU(2)--monopole in five dimensions. The Schr\"odinger equation for this system is separable in the hyperspherical and parabolic coordinates.…
This paper deals with a dynamical system that generalizes the Kepler-Coulomb system and the Hartmann system. It is shown that the Schr\"odinger equation for this generalized Kepler-Coulomb system can be separated in prolate spheroidal…
An explicit expression for the general bivariate Krawtchouk polynomials is obtained in terms of the standard Krawtchouk and dual Hahn polynomials. The bivariate Krawtchouk polynomials occur as matrix elements of the unitary reducible…
This paper deals with the dynamical system that generalizes the MIC-Kepler system. It is shown that the Schr\"{o}dinger equation for this generalized MIC-Kepler system can be separated in prolate spheroidal coordinates. The coefficients of…
In this report, in the framework of an analytical approach and with help of the generalized version of the Hurwitz transformation the five-dimensional SU(2)--monopole model is constructed from the eight-dimensional quantum oscillator. The…
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…
The symmetry structure of twodimensional nonlinear isotropic oscillator, introduced in Physica D237 (2008) 505, is discussed. It is shown that it possesses three independent integrals of motion which can be chosen in such a way that they…
The oscillator bases expansion stands as an efficient approximation method for the time-independent Schr\"odinger equation. The method, originally formulated with one non-linear variational parameter, can be extended to incorporate two such…
A non--Abelian $SU(2)$ model is constructed for a five--dimensional bound system "charge--dyon" on the basis of the Hurwitz--transformed eight--dimensional isotropic quantum oscillator. The principle of dyon--oscillator duality is…
In this paper, we investigate a two dimensional isotropic harmonic oscillator on a time-dependent spherical background. The effect of the background can be represented as a minimally coupled field to the oscillator's Hamiltonian. For a…
Clebsch-Gordan coefficients of SU(2) and SU(1,1) are defined as eigenfunctions of a linear operator acting on the tensor product of the Hilbert spaces for two irreps of these groups. The shifted harmonic approximation is then used to solve…
We show that the even- resp. odd-dimensional Schoenberg coefficients in Gegenbauer expansions of isotropic positive definite functions on the d-sphere can be expressed as linear combinations of Fourier resp. Legendre coefficients, and we…
We characterize the angular polyspectra, of arbitrary order, associated with isotropic fields defined on the sphere S^2. Our techniques rely heavily on group representation theory, and specifically on the properties of Wigner matrices and…
We show that the oscillators on a sphere and pseudosphere are related, by the so-called Bohlin transformation, with the Coulomb systems on the pseudosphere: the even states of an oscillator yields the conventional Coulomb system on…
A new integrable generalization to the 2D sphere $S^2$ and to the hyperbolic space $H^2$ of the 2D Euclidean anisotropic oscillator Hamiltonian with Rosochatius (centrifugal) terms is presented, and its curved integral of the motion is…
The rotations, boosts, and translations in an N^2-dimensional spacetime are shown to be related to the fundamental commutators, anticommutators, and Clebsch-Gordan coefficients, respectively, of SU(N).
We investigated numerically an Ising model coupled to two-dimensional Euclidean gravity with spherical topology, using Regge calculus with the $dl/l$ path-integral measure to discretize the gravitational interaction. Previous studies of…