Approximate solutions of the nonlinear Schrodinger equation for ground and excited states of Bose-Einstein condensates

I present simple analytical methods for computing the properties of ground and excited states of Bose-Einstein condensates, and compare their results to extensive numerical simulations. I consider the effect of vortices in the condensate for both positive and negative scattering lengths, a , and find an analytical expression for the large-N0 limit of the vortex critical frequency for a > 0, by approximate solution of the timeindependent nonlinear Schro dinger equation.