  We devise a new and highly accurate quantization procedure for the inner
product representation, both in configuration and momentum space. Utilizing the
representation $\Psi(\xi) = \sum_{i}a_i[E]\xi^i R_{\beta}(\xi)$, for an
appropriate reference function, $R_{\beta}(\xi)$, we demonstrate that the
(convergent) zeroes of the coefficient functions, $a_i[E] = 0$, approximate the
exact bound/resonance state energies with increasing accuracy as $i \to
\infty$. The validity of the approach is shown to be based on an extension of
the Hill determinant quantization procedure. Our method has been applied, with
remarkable success, to various quantum mechanical problems.
