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Paper   IPM / Physic / 7647
School of Physics
  Title:   Landau Levels on the Hyperbolic Plane
1.  H. Fakhri
2.  M. Shariati
  Status:   Published
  Journal: J. Phys. A: Math. Gen.
  Vol.:  37
  Year:  2004
  Pages:   L539-L545
  Supported by:  IPM
The quantum states of a spinless charged particle on a hyperbolic plane in the presence of a uniform magnetic field with a generalized quantization condition are proved to be the bases of the irreducible Hilbert representation spaces of the Lie algebra u(1,1)with the explicit form of the Lie algebra generators is extracted. It is also shown that the energy has an infinite-fold degeneracy in each of the representation spaces which are allocated to the different values of the magnetic field strength. Based on the simultaneous shift of two parameters, it is also noted that the quantum states realize the representations of Lie algebra u(2) by shifting the magnetic field strength.

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