  Classical properties of 1/4 BPS dyons were previously well understood both in
field theory context and in string theory context. Its quantum properties,
however, have been more difficult to probe, although the elementary information
of the supermultiplet structures is known from a perturbative construction.
Recently, a low energy effective theory of monopoles was constructed and argued
to contain these dyons as quantum bound states. In this paper, we find these
dyonic bound states explicitly in the N=4 supersymmetric low energy effective
theory. After identifying the correct angular momentum operators, we motivate
an anti-self-dual ansatz for all BPS bound states. The wavefunctions are found
explicitly, whose spin contents and degeneracies match exactly the expected
results.
