On Quantization, the Generalized Schrödinger Equation and Classical Mechanics
Abstract
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 Schrödinger 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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2012
- DOI:
- 10.48550/arXiv.1212.6784
- arXiv:
- arXiv:1212.6784
- Bibcode:
- 2012arXiv1212.6784J
- Keywords:
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- Quantum Physics;
- Mathematical Physics;
- Nonlinear Sciences - Chaotic Dynamics
- E-Print:
- 8 pages