MAGNETIC GROUP ON THE PSEUDOSPHERE

The quantum mechanics of a particle moving on a pseudosphere under the action of a constant magnetic field is studied from an algebraic point of view. The magnetic group on the pseudosphere is SU(1,1). The Hilbert space for the discrete part of the spectrum is investigated. The eigenstates of the non-compact operators (the hyperbolic magnetic translators) are constructed and shown to be expressible as continuous superpositions of coherent states. The planar limit of both the algebra and the eigenstates is analyzed. Some possible applications are briefly outlined.