  Bound state solutions of the Schrodinger Equation for the $-a/r^2$ potential
have been presented recently for both the weak and strong coupling cases.
However, Shortley in 1931 and Landau and Lifshitz in 1958 claimed that no bound
state solutions exist for the weak coupling case when $0 < 2ma/\hbar^2 <= (l +
1/2)^2$. We demonstrate that one bound state solution can exist for each
angular momentum state l, and that a complete orthogonal set of continuum
eigenfunctions orthogonal to the bound state eigenfunction can be constructed
when $l(l+ 1) < 2ma/\hbar^2 <= (l + 1/2)^2$. We show that Shortley's argument
is spurious due to his neglecting a boundary term arising from the momentum
operator and that the Landau and Lifshitz claim is based on a restrictive
fitting of the exterior solution to an interior spherical well. Instead, to
each weak coupling, a, we find a unique interior well strength $V_{in} =
-a'/ro^2$ which yields a finite bound state. In particular for the l = 0 case
the well strength is given by: $2ma'/\hbar^2 = 1.3734 + 2.2265*(1/4 -
2ma'/\hbar^2)^{1/2}$.
