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.Comment: 46 pages; harvmac; a typo fixed and a footnote adde
