Excited stationary states of trapped Bose-Einstein condensates
  We investigate the excited stationary states of Bose-Einstein condensates trapped in harmonic potentials. We derive simple analytical approximations of the first few eigenstates of the associated time-independent one-dimensional Gross-Pitaevskii equation and their energies. Our results are excited state generalizations of the Thomas-Fermi approximation of the ground state. 
John A. Vaccaro, Ole Steuernagel and Ben Lorimer