A class of closed solutions for the bogoliubov excitations on smooth ground state of a trapped Bose-Einstein condensate

摘要

Bogoliubov-de Gennes equations (BdGEs) for collective excitations from a trapped Bose-Einstein condensate described by a spatially smooth ground-state wavefunction can be treated analytically. A new class of closed solutions for the BdGEs is obtained for the one-dimensional (1D) and 3D spherically harmonic traps. The solutions of zeroenergy mode of the BdGEs axe also provided. The eigenfunctions of the excitations consist of zero-energy mode, zero-quantum-number mode and entire excitation modes when the approximate ground state is a background Bose gas sea.