Abstract Title: Macroscopic Quantum Mechanics in Planetary Systems: The Structuring of Planetary Orbits by Resonant Exponential-Functions This thesis investigates the discrete structuring of planetary orbits and transneptunic objects in the context of macroscopic wave mechanics. Based on the classical Laplace operator and the mathematical analogy to quantum mechanical potential problems, it is shown that the orbital distances of the solar system can be interpreted as resonance nodes of a standing wave field. By linearizing the path data via a logarithmic metric, a system of discrete quantum numbers - so-called dimensional numbers (n) - is derived. In order to clean up local discontinuities in the outer solar system, the inner Kuiper belt together with Pluto is defined as a collective, smeared quantum state (n = 8.88). Based on this, a closed, nonlinear, generating first-order differential equation n(k+1) = f (n(k)) is formulated. By means of a modified Gaussian distribution, whose resonance node lies in the gravitational barycenter of the system (between Jupiter and Saturn), a deterministic recursion of the orbital main shells succeeds. The mathematical model reproduces both the inner rock planets and the gas giants, extending the system consistently to the extreme transneptunian objects Eris and FarFarOut. The results support the hypothesis that the spatial arrangement of celestial bodies is not a result of purely stochastic accretion processes, but obeys a fundamental, self-referential resonance metric of space.
Klaus Piontzik (Sun,) studied this question.