  Making use of the well-known phase space reduction in the lowest Landau
level(LLL), we show that the Laughlin wave function for the $\nu = {1\over m}$
case can be obtained exactly as a coherent state representation of an one
dimensional $(1D)$ wave function. The $1D$ system consists of $m$ copies of
free fermions associated with each of the $N$ electrons, confined in a common
harmonic well potential. Interestingly, the condition for this exact
correspondence is found to incorporate Jain's parton picture. We argue that,
this correspondence between the free fermions and quantum Hall effect is due to
the mapping of the $1D$ system under consideration, to the Gaussian unitary
ensemble in the random matrix theory.
