On Quantization, the Generalized Schr\"odinger Equation and Classical Mechanics

Using a new state-dependent, $\lambda$-deformable, linear functional operator, ${\mathcal{Q}}_{\psi }^{\lambda }$, which presents a natural $C^{\mathrm{\infty }}$ deformation of quantization, we obtain a uniquely selected non–linear, integro–differential Generalized Schr"odinger equation. The case ${\cal Q}{\psi}^{1}$reproduceslinearquantummechanics,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.