Quantum Physics

   

SunQM-6s9: Reformulating Schrodinger Equation/Solution to Show Its r-1D Reversed-Diffusion Character for Solar System’s {N,n} QM Structure Formation (Drafted in January 2020)

Authors: Yi Cao

A pre-Sun ball (quantum) collapse process can be intuitively thought as a (mass) reversed diffusion process in r-dimension. It has been noticed for many years (and by many QM scientists) that there is similarity between Schrodinger equation and a diffusion equation. In the current paper, 1) By using Euler formula’s complex space (that was defined as the "i-space" in this article), I reformulated the expression of the orbital energy E = K + V to be K = Kθφ + iKr and V = Vθφ + iVr , and then E = K + iV* = (Kθφ + Vr) + i(Kr + Vθφ); 2) I assumed that a plane-like wave can be used as the solution (i.e., the wave function) of Schrodinger equation (either for an H-atom, or for Solar system), and then separate this 3D plane-like wave into two parts, one in r-1D only, and one in θφ-2D only; 3) Accordingly, (by guessing, not by the mathematical deduction), I separated a traditional spherical 3D Schrodinger equation into two: one in θφ-2D only, and one in r-1D only; 4) While the θφ-2D-only Schrodinger equation is almost same as the traditional one, the r-1D-only Schrodinger equation can be further degenerated into a r-1D diffusion equation with the diffusion constant D= ℏ/2m ; 5) At a citizen-scientist-level, I confirmed that the θφ-2D plane-like wave function is the solution of the θφ-2D-only Schrodinger equation, and the r-1D plane-like wave function is the solution of the r-1D-only Schrodinger equation as well as the r-1D diffusion equation. In this way, I demonstrated that Schrodinger equation may can be directly degenerated into a diffusion equation (at least in r-dimension). Furthermore, according to this explanation, the other QM scientists’ previous result of D → iℏ/2m may can be re-explained as that, the diffusion constant D= ℏ/2m not only radially diffuses in r-1D, but also laterally diffuses in θφ-2D through RF (RotaFusion, or rotation diffusion). If this explanation is correct, then the function of analyzing the E = K + V in an "i-space" maybe is to filter out the RF (the lateral diffusion) in θφ-2D, so that a pure r-1D diffusion can be obtained. Even I am not sure whether this method is correct or not, this deduction certainly opened a new route to reformulate Schrodinger equation and solution. This work may also have created a completely new way to study the relationship between the RF and the energy of the orbital motion. (Note: This article was drafted in Jan. 2020).

Comments: 23 Pages.

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[v1] 2023-12-19 20:21:59

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