  Using a new state-dependent, $\lambda$-deformable, linear functional
operator, ${\cal Q}_{\psi}^{\lambda}$, which presents a natural $C^{\infty}$
deformation of quantization, we obtain a uniquely selected non--linear,
integro--differential Generalized Schr\"odinger equation. The case ${\cal
Q}_{\psi}^{1}$ reproduces linear quantum mechanics, whereas ${\cal
Q}_{\psi}^{0}$ admits an exact dynamic, energetic and measurement theoretic
{\em reproduction} of classical mechanics. All solutions to the resulting
classical wave equation are given and we show that functionally chaotic
dynamics exists.
