  We derive a set of equations for the wavefunction describing the marginal
bound state of a single D0-brane with a single D4-brane. These are equations
determining the vacuum of an N=8 abelian gauge theory with a charged
hypermultiplet. We then solve these equations for the most general possible
zero-energy solution using a Taylor series. We find that there are an infinite
number of such solutions of which only one must be normalizable. We explore the
structure of a normalizable solution under the assumption of an asymptotic
expansion. Even the leading terms in the asymptotic series, which should
reflect the supergravity solution, are unusual. Through the $Spin(5)$ flavor
symmetry, the modes which are massive at long distance actually influence the
leading behavior. Lastly, we show that the vacuum equations can quite
remarkably be reduced to a single equation involving one unknown function. The
resulting equation has a surprisingly simple and suggestive form.
