Abstract
We propose a method for finding analytical solutions of the
Bogoliubov–de Gennes (BdG) equations for the low-lying collective
excitations in a harmonically trapped Bose-Einstein condensate beyond
the Thomas-Fermi limit. We first use a simple variational wave function
for ground state to eliminate the divergence at the boundary layer of
the condensate, which appears in the Thomas-Fermi approximation. We then
solve the BdG equations analytically and obtain explicit and
divergence-free expressions for the eigenvalues and eigenfunctions of
the excitations for the traps with spherical and cylindrical symmetries.
The solutions of the zero-energy mode of the BdG equations are also
presented.
| Original language | English |
|---|---|
| Article number | 063608 |
| Journal | Physical Review A |
| Volume | 69 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 15 Jun 2004 |
