**Authors:** Yi Cao

Asteroid belt is explained as the leftover “ring stain” of the once out-flying ice-rock mixture fragments (driven by the expansion of the ice-evap-line). The cold-KBO of Kuiper belt is explained as the “ring stain” of the current out-flying methane-ice mixture fragments (driven by the expansion of methane-evap-line, or the solar wind stop line). Using the normalized radial probability function r^2 * |R(n,l=n-1)|^2 = [r/rn * exp(1 - r/rn)]^(2*n), we calculated out that (at the normalized probability ≥ 0.1), Asteroid belt at {1,8//6} = {0,48//6} has a probability peak at n = 48, with the peak range = 2.7 ±0.6 AU, and Kuiper belt at {3,1//6} = {0,192//6} has a probability peak at n = 192, with the peak range = 43 ±5 AU. Using θ-dimension probability formula [sin(θ)]^[2(n-1)] ≥ 0.01, we calculated out that the n=48 belt has the collective orbits’ inclination range < 17.8 degree, and b=192 belt has the collective orbits’ inclination range < 8.9 degree. These calculated results fit to the Asteroid belt’s and the cold-KBO’s experimental data perfectly. Then we proposed a new concept: “Eigen quantum number n’ ” is the maximum n’ that can describe one orbit space’s > 90% mass in a single |nLL> = |n’,n’-1,n’-1> QM state. So n=48 and n=192 are the Eigen description for Asteroid belt and the cold-KBO. Using the Eigen n, the four undiscovered {3,n=2..5//6} belts (if they did not form planets) ’s r ± Δr and Δθ’ ranges are also predicted. Using the Eigen n, the Solar {N=1..4,n//6} region’s r-dimensional mass distribution was described by r^2*|R(n,l)|^2 either at each n shell level, or at each N super-shell level, or at the level of treating all N super-shells as a single entity. The evolution of r-dimensional mass distribution in Solar system (driven by the expansion of rock-evap-line and ice-evap-line) is discussed. The result suggested that any sub-Eigen n’ description for an Eigen QM state will be a low resolution and more broad description, and any above Eigen n’ description for an Eigen QM state will be a high resolution but needs many linearly combined QM states.

**Comments:** 22 Pages.

**Download:** **PDF**

[v1] 2019-09-12 13:11:10

**Unique-IP document downloads:** 24 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful. *