  Bilayer quantum Hall system (BLQH) differ from its single layer counterparts
(SLQH) by its symmetry breaking ground state and associated neutral gapless
mode in the pseudo-spin sector. Due to the gapless mode, qualitatively good
groundstate and low energy excited state wavefunctions at any finite distance
is still unknown. We investigate this important open problem by the Composite
Boson (CB) theory developed by one of the authors to study BLQH systematically.
We derive the ground state, quasi-hole and a pair of quasihole wavefunctions
from the CB theory and its dual action. We find that the ground state
wavefunction differs from the well known $ (111) $ wavefunction at any finite $
d $. In addition to commonly known multiplicative factors, the quasi-hole and a
pair of quasi-holes wavefunctions also contain non-trivial normalization
factors multiplying the correct ground state wavefunction. All the distance
dependencies in all the wavefunctions are encoded in the spin part of the
ground state wavefunction. The instability encoded in the spin part of the
groundstate wavefunction leads to the pseudo-spin density wave formation
proposed by one of the authors previously. Some subtleties related to the
Lowest Landau Level (LLL) projection of the wavefunctions are briefly
discussed.
