17 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 Stark effect in the charge-dyon system
The linear Stark effect in the MIC-Kepler problem describing the interaction
of charged particle with Dirac's dyon is considered. It is shown that constant
homogeneous electric field completely removes the degeneracy of the energy
levels on azimuth quantum numberComment: 6 page
Relationship between quantum mechanics with and without monopoles
We show that the inclusion of the monopole field in the three- and
five-dimensional spherically symmetric quantum mechanical systems, supplied by
the addition of the special centrifugal term, does not yield any change in the
radial wavefunction and in the functional dependence of the energy spectra on
quantum numbers. The only change in the spectrum is the lift of the range of
the total and azimuth quantum numbers. The changes in the angular part
wavefunction are independent of the specific choice of the (central) potential.
We also present the integrable model of the spherical oscillator which is
different from the Higgs oscillator.Comment: LaTeX, 6 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
Hyperboloid, instanton, oscillator
We suggest the exactly solvable model of the oscillator on a four-dimensional
hyperboloid which interacts with a SU(2) instanton. We calculate its
wavefunctions and spectrum.Comment: 6 pages, PACS numbers: 03.65-w, 11.30.P