  Unlike the situation for the 1d Dirac delta derivative Schrodinger pseudo
potential (SPP) and the 2d Dirac delta SPP, where the indeterminacy originates
from a lack of scale in the first and both a lack of scale as well as the wave
function not being well defined at the support of the generalized function SPP;
the obstruction in 3d Euclidean space for the Schrodinger equation with the
Dirac delta as a SPP only comes from the wave function (the $L^2$ bound sate
solution) being singular at the compact point support of the Dirac delta
function (measure). The problem is solved here in a completely mathematically
rigorous manner with no recourse to renormalization nor regularization. The
method involves a distributionally generalized version of the Schrodinger
theory as developed by the author, which regards the formal symbol "$H\psi$" as
an element of the space of distributions, the topological dual vector space to
the space of smooth functions with compact support. Two main facts come to
light. The first is the bound state energy of such a system can be calculated
in a well-posed context, the value of which agrees with both the mathematical
and theoretical physics literature. The second is that there is then a rigorous
distributional version of the Hellmann-Feynman theorem.
