**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.

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

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