1212.6784 (K. R. W. Jones)

On Quantization, the Generalized Schrödinger Equation and Classical
Mechanics    [PDF]

K. R. W. Jones

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.

View original: http://arxiv.org/abs/1212.6784