70 research outputs found
Oscillator potential for the four-dimensional Hall effect
We suggest the exactly solvable model of oscillator on the four-dimensional
sphere interacting with the SU(2) Yang monopole. We show, that the properties
of the model essentially depend on the monopole charge.Comment: 4 page
4D singular oscillator and generalized MIC-Kepler system
It is shown that the generalized MIC-Kepler system and four-dimensional
singular oscillator are dual to each other and the duality transformation is
the generalized version of the Kustaanheimo-Stiefel transformation.Comment: 6 page
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
Park--Tarter Matrix for a Dyon--Dyon System
The problem of separation of variables in a dyon--dyon system is discussed. A
linear transformation is obtained between fundamental bases of this system.
Comparison of the dyon--dyon system with a 4D isotropic oscillator is carried
out.Comment: 9 pages, LaTeX fil
Coulomb-oscillator duality in spaces of constant curvature
In this paper we construct generalizations to spheres of the well known
Levi-Civita, Kustaanheimo-Steifel and Hurwitz regularizing transformations in
Euclidean spaces of dimensions 2, 3 and 5. The corresponding classical and
quantum mechanical analogues of the Kepler-Coulomb problem on these spheres are
discussed.Comment: 33 pages, LaTeX fil
Nondegenerate 3D complex Euclidean superintegrable systems and algebraic varieties
A classical (or quantum) second order superintegrable system is an integrable
n-dimensional Hamiltonian system with potential that admits 2n-1 functionally
independent second order constants of the motion polynomial in the momenta, the
maximum possible. Such systems have remarkable properties: multi-integrability
and multi-separability, an algebra of higher order symmetries whose
representation theory yields spectral information about the Schroedinger
operator, deep connections with special functions and with QES systems. Here we
announce a complete classification of nondegenerate (i.e., 4-parameter)
potentials for complex Euclidean 3-space. We characterize the possible
superintegrable systems as points on an algebraic variety in 10 variables
subject to six quadratic polynomial constraints. The Euclidean group acts on
the variety such that two points determine the same superintegrable system if
and only if they lie on the same leaf of the foliation. There are exactly 10
nondegenerate potentials.Comment: 35 page
- …