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

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

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

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