### Abstract

We define the Landau problem on two-dimensional ellipsoid, hyperboloid and paraboloid of revolution. Starting from the two-center McIntosh-Cisneros-Zwanziger (MICZ)-Kepler system and making the reduction into these two-dimensional surfaces, we obtain the Hamiltonians of the charged particle moving on the corresponding surface of revolution in the magnetic field conserving the symmetry of the two-dimensional surface (Landau problem). For each case we figure out the values of parameter for which the qualitative character of the motion coincides with that of a free particle moving on the same two-dimensional surface. For the case of finite trajectories we construct the action-angle variables.

Original language | English |
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Article number | 1450148 |

Journal | Modern Physics Letters A |

Volume | 29 |

Issue number | 29 |

DOIs | |

Publication status | Published - 21 Sep 2014 |

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### Keywords

- Hamilton-Jacobi method
- Landau problem
- Magnetic monopoles

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Nuclear and High Energy Physics

### Cite this

*Modern Physics Letters A*,

*29*(29), [1450148]. https://doi.org/10.1142/S021773231450148X