  The Half-Transform Ansatz (HTA) is a proposed method to solve hyper-geometric
equations in Quantum Phase Space by transforming a differential operator to an
algebraic variable and including a specific exponential factor in the wave
function, but the mechanism which provides this solution scheme is not known.
Analysis of the HTA's application to the Hydrogen atom suggests an underlying
mechanism which the HTA is a part of. Observations of exponential factors that
act on the wave function naturally suggest modeling quantum operator
definitions as a point on a Riemannian manifold in the 4D Operator Space, a
novel idea we call the Operator Space Manifold Theory. Expanding on this
concept, we find the true nature of the HTA and how Operator Space Manifold
Theory can be used to describe and solve quantum systems by manipulating how a
quantum state perceives position and momentum.
