Relationship between quantum mechanics with and without monopoles

TL;DR

This paper investigates how the inclusion of monopole fields affects the quantum mechanics of spherically symmetric systems, finding that it alters quantum number ranges but not radial wavefunctions or energy dependence.

Contribution

It demonstrates that monopoles do not change radial wavefunctions or energy spectra dependence, only the quantum number ranges, and introduces a new integrable spherical oscillator model.

Findings

Monopoles do not affect radial wavefunctions.

Energy spectra dependence remains unchanged.

Quantum number ranges are modified by monopoles.

Abstract

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.