 93198 Iengo R., Li D.
 Quantum mechanics and quantum Hall effect on Riemann surfaces
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Jul 9, 93

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Abstract. The quantum mechanics of a system of charged
particles interacting with a magnetic field
on Riemann surfaces is studied.
We explicitly construct the wave functions of ground states
in the case of a metric proportional to the Chern form
of the $\theta$bundle, and the wave functions of
the Landau levels in the case of the the Poincar{\' e} metric.
The degeneracy of the the Landau levels is obtained by using
the RiemannRoch theorem. Then we construct the Laughlin wave function
on Riemann surfaces and discuss the mathematical structure
hidden in the Laughlin wave function.
Moreover the degeneracy of the Laughlin states is also
discussed.
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