  New trial wave functions corresponding to half filling quantum Hall states
are proposed. These wave functions are constructed by first pairing up the
quasielectrons of the 1/3 Laughlin quantum Hall state, with the same relative
angular momentum for each pair, and then making the paired quasielectrons
condense into a 1/4 Laughlin state. The quasiparticle excitations of the
proposed wave functions carry $\pm1/4$ of electron charge, and obey Abelian
fractional statistics. In the spherical geometry, the total flux quanta
$N_{\phi}$ is shown to be related to the number of electrons $N$ by $N_{\phi} =
2N-(5-q)$ with $q$ being the relative angular momentum between the
quasielectrons in each pair which takes values of non-negative even integers.
The overlaps are calculated between the proposed trial wave functions,
including the ground state, quasiexciton states, and quasihole states, and the
exact states of the finite size systems at $N_{\phi} = 2N-3$. The near unity
overlaps are obtained in the lowest Landau level, while the moderate overlaps
are obtained in the second Landau level. The relevance of the wave functions to
the yet to be discovered fractional quantum Hall effect in the lowest Landau
level, as well as the 5/2 quantum Hall effect is also discussed.
