On Quantization, the Generalized Schrödinger Equation and Classical Mechanics

Abstract

Using a new state-dependent, $\lambda$-deformable, linear functional operator, ${\mathcal{Q}}_{\psi }^{\lambda }$, which presents a natural $C^{\infty }$ deformation of quantization, we obtain a uniquely selected non--linear, integro--differential Generalized Schrödinger equation. The case ${\mathcal{Q}}_{\psi }^1$ reproduces linear quantum mechanics, whereas ${\mathcal{Q}}_{\psi }^0$ 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.

8 pages