  We propose a derivative operator formed as a function of derivatives of the
electron coordinates. When the derivative operator is applied to the Laughlin
wave function, two new wave functions in the lowest Landau level at filling
factor 1/2 are generated. For systems of 4, 6, and 8 electrons in spherical
geometry, it is shown that the first wave function has nearly unity overlap
with the particle-hole conjugate of the Moore-Read Pfaffian wave function,
therefore together with the Moore-Read Pfaffian state forms a particle-hole
conjugate pair. The second wave function has essentially perfect particle-hole
symmetry itself, with a positive parity when the number of electron pairs N/2
is an even integer and and a negative parity when N/2 is an odd integer. An
equivalent form suggests the first wave function forms a f-wave pairing of
composite fermions, and the second wave function forms a p-wave pairing. The
corresponding Non-Abelian statistics quasiparticle wave functions are also
proposed.
