  The theory of Bose-Einstein condensation in a two-dimensional(2D) harmonic
trap is developed from 2D Gross-Pitaevskii equation. The 2D interaction
strength is obtained from a 2D collision theory.
  We show the realization of 2D condensation of trapped Bose atoms directly by
obtaining the stable solutions for the condensate wave function from the 2D
Gross-Pitaevskii equation. We calculate the ground-state energy of the 2D
system, and also the wave function of the 2D vortex state. In particular, the
2D energy state becomes less stable than the 3D case with the number of trapped
atoms. The results of the 2D Bose condensation are also compared with those of
the well-known 3D case.
