ANALYTIC CALCULATIONS OF TRIAL WAVE-FUNCTIONS OF THE FRACTIONAL QUANTUM HALL-EFFECT ON THE SPHERE

We present a framework for analytic calculations of the hierarchical w ave functions and the composite fermion wave functions in the fraction al quantum Hall effect on the sphere by using projective coordinates. Then we calculate the overlaps between these two wave functions at var ious fillings and small numbers of electrons. We find that the overlap s are almost equal to 1. This gives further evidence that two theories of the fractional quantum Hall effect, the hierarchical theory and th e composite fermion theory, are physically equivalent.