91 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
The generalized MIC-Kepler system
This paper deals with 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 spherical and parabolic coordinates. The
spectral problem in spherical and parabolic coordinates is solved.Comment: 8 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
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