## “School of Physic”

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Paper   IPM / Physic / 7647
School of Physics
Title:   Landau Levels on the Hyperbolic Plane
Author(s):
 1 H. Fakhri 2 M. Shariati
Status:   Published
Journal: J. Phys. A: Math. Gen.
Vol.:  37
Year:  2004
Pages:   L539-L545
Supported by:  IPM
Abstract:
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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