## Macroscopic Schroedinger quantization of the early chaotic solar system
Classical mechanics is compatible with Schroedinger's equation without any approximation of the standard WKB semiclassical quantum type. In order to illustrate this property, we propose an exact Schroedinger theory for Nottale's macro-quantization of the solar system in which neither semiclassical approximations nor the probabilistic Born postulate are assumed. We point out the existence and properties of radial-velocity proto-planetary solitons that describe the swarm of chaotic orbits supposed to dominate at the later stage of the solar system formation, in accordance with Nottale's scale-relativity theory.
This article contains no SIMBAD objects. ## Contents- 1. Introduction
- 2. Quantum probability and complex wavefunctions
- 3. Madelung's central-field problem
- 4. Classical interpretation of Schroedinger equation
- 5. The Kepler-Madelung system
- 6. Schroedinger equation on the scale of the solar system
- 7. Conclusion
- Acknowledgements
- References
© European Southern Observatory (ESO) 1998 Online publication: August 6, 1998 |