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; Volume 3 (2023)
21. Dongfang Brief General Solutions to Congruence Equations
The Chinese remainder theorem gives the general solution of the strongly constrained linear congruence system of module pairwise coprime, but it can not directly give the minimum natural number solution of the system of congruence equations. Nor does it clarify the necessary and sufficient conditions for the weak constrained linear congruence equations with different modules to have a solution and the formula of weakly constrained general solution. Here, the Chinese remainder theorem is promoted, clarifying the conditional equations for the existence of solutions to weakly constrained systems of linear congruence equations. The new concise formulas are utilized to express the general solutions of strongly constrained congruence systems and weakly constrained congruence systems, thereby improving the theory of system of congruence equations. Then, the concise steps are provided to directly construct the general solutions of linear strongly constrained and weakly constrained system of congruence equations, in order to promote the popularization of congruence equation theory on a wider range. Finally, the question of whether a universal method for solving the rational number solution of the minimum number of digits for an indefinite system of equations exists was brought up.
Citation: Dongfang, X. D. Dongfang Brief General Solutions to Congruence Equations. Mathematics & Nature 3, 202301 (2023).
22. Dongfang Special Entangled Spherical Harmonic Functions
The spherical harmonic partial differential equation is usually solved by variable separation. When the magnetic quantum number m of the obtained Legendre spherical harmonic function is 0, the Legendre spherical harmonic function degenerates into the Legendre function of angle θ. This is a deduction that may seem rigorous in mathematics but is actually not true. Replace the cosine function of angle θ in the Legendre function with the product of the sine function of angle θ and the sine function or cosine function of angle φ, and obtain two special binary trigonometric series called special entanglement functions that satisfy the spherical harmonic partial differential equation. According to the basic principles of differential equation, the linear combination of three special spherical harmonic functions is a local special general solution of the spherical harmonic partial differential equation with a magnetic quantum number m of 0. However, the normalization condition cannot determine the three undetermined coefficients and therefore cannot determine the specific spherical harmonic function. The established physical conclusions based on spherical harmonic functions, especially the mathematical principles of quantum mechanics, need to supplement the definite solution conditions of spherical harmonic partial differential equations and rewrite them after determining specific exact solutions.
Citation: Dongfang, X. D. Dongfang Special Entangled Spherical Harmonic Functions. Mathematics & Nature 3, 202302 (2023).
23. Dongfang Special Entangled Solution of Schrödinger Hydrogen Equation
The textbook solutions of Schrödinger equations are usually represented as the combination of multiple special function symbols, resulting in a large number of missing exact solutions not being discovered. Taking the Schrödinger wave function of a hydrogen atom as an example, regressing to the analytical expression that can be extended and programmed for testing, two types of special entangled wave functions that have not been described by established theories have been discovered. Specifically, when the magnetic quantum number is 0, the traditional Schrödinger wave function degenerates into a binary function about radial variables r and angle θ without angles φ. The conclusion of this reasoning process, which seems very rigorous in the traditional sense, is actually extremely untrue. The Schrödinger equation for hydrogen atoms has two types of special entangled solutions with magnetic quantum numbers of 0, and the sine and cosine functions of angle φ are included in it, implying that there are other unknown wave functions that satisfy the Schrödinger equation and even affect the energy eigenvalue formula. The three-dimensional function image of the special entangled solution of the hydrogen atom Schrödinger equation is further drawn. The results show intuitively and clearly that there is no one-to-one correspondence between the zero or extreme point of the modulus function of the ternary function and that of the square of the modulus function of the ternary function. It is concluded that the definition of the square of the wave function modulus as the probability density function lacks causality, and it is an urgent problem to derive the probability density function according to the basic principle.
Citation: Dongfang, X. D. Dongfang Special Entangled Solution of Schrödinger Hydrogen Equation. Mathematics & Nature 3, 202303 (2023).
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PS: Why do contemporary breakthrough papers choose to be published in self media journals? This groundbreaking paper based on Dongfang Special Entangled Spherical Harmonic Functions was written within a week, aiming to reveal the serious confidence issues hidden in quantum mechanics and promote significant changes in scientific theory. Before writing this paper, Nature Physics had sent a solicitation letter to the author, mainly inquiring about the author's recent research status, the title and abstract of the paper the author plans to submit to Nature Physics, and the estimated time required for the author to complete the research project. However, based on the fact that breakthrough papers submitted to Nature Physics in the past were all rejected, the author infers that Nature Physics is not genuinely soliciting submissions from the author, but is tentatively attempting to steal the core scientific principles needed to create a new Newtonian era and achieve the plan of revitalizing the country through science. The author did not reply to this solicitation letter and deleted it as spam. After careful consideration, the author decided to submit the new important paper to Nature Physics for the last time, both to confirm his personal views on Nature and to respond to readers' doubts about the author's choice of publication method. The article submission number is NPHYS-2024-06-01859. In the submitted version, the author removed important experimental suggestions written after the first equation. The reason for doing so is out of scientific belief and responsibility. The Nature journal has an absolute advantage in enticing the world to submit major breakthrough research results in a timely manner due to its enormous influence. Editors can efficiently assist domestic scientists in plagiarizing breakthrough discoveries that have changed the scientific world. Although the Nature team and its complex members, with their current level of scientific theory, do not have the ability to perfect partial differential equation theory and discover the fundamental principles of unified macroscopic and microscopic quantum theory after plagiarizing special entanglement function theory, if they shift their focus to plagiarizing breakthrough experimental ideas, profound misunderstandings may occur, leading science in a new wrong direction once again. The author agreed to share this paper on Research Square when submitting it to Nature Physics. After 18 days of detailed dissection by numerous personnel, the editor of Nature Physics informed the author that their decision was not to send the paper for external review. This is expected. Readers should be aware of the reality of the scientific world. On the one hand, because scientific theories play a crucial role in the field of ideology, scientific research in many countries is actually tied to political tasks. On the one hand, due to the enormous benefits of scientific research, some individuals who originally lacked the ability to conduct scientific research actively infiltrate the editorial and peer review teams of renowned academic journals, often plagiarizing and selling breakthrough submissions to maximize their personal interests. In the field of science, it usually takes a hundred or even hundreds of years for a few pioneering researchers to emerge. If you are a pioneering researcher, you will inevitably face numerous despicable opponents everywhere, so never expect your breakthrough research results to be accepted by reputable academic journals such as Nature. Instead, you should consider how to publicly disclose your research results and effectively do anti-theft and anti murder work, ensuring that great discoveries are not contaminated by ignorant and unethical editors or peer reviewers, and ensuring that readers with independent research capabilities are timely informed of new discoveries and develop theories correctly. By reading numerous groundbreaking papers by authors, future pioneering researchers can also experience unique writing techniques that deter scientific thieves. However, there will always be just scientists in the world, which is the fundamental guarantee for the continuous progress of human civilization. |
24. Dongfang Special Entangled Schrödinger Wave Function of Hydrogen
The textbook solutions of Schrödinger equations are usually represented as the combination of multiple special function symbols, resulting in a large number of missing exact solutions not being discovered. Taking the Schrödinger wave function of a hydrogen atom as an example, regressing to the analytical expression that can be extended and programmed for testing, two types of special entangled wave functions that have not been described by established theories have been discovered. Specifically, when the magnetic quantum number is 0, the traditional Schrödinger wave function degenerates into a binary function about radial variables r and angle θ without angles φ. The conclusion of this reasoning process, which seems very rigorous in the traditional sense, is actually extremely untrue. The Schrödinger equation for hydrogen atoms has two types of special entangled solutions with magnetic quantum numbers of 0, and the sine and cosine functions of angle φ are included in it, implying that there are other unknown wave functions that satisfy the Schrödinger equation and even affect the energy eigenvalue formula. The three-dimensional function image of the special entangled solution of the hydrogen atom Schrödinger equation is further drawn. The results show intuitively and clearly that there is no one-to-one correspondence between the zero or extreme point of the modulus function of the ternary function and that of the square of the modulus function of the ternary function. It is concluded that the definition of the square of the wave function modulus as the probability density function lacks causality, and it is an urgent problem to derive the probability density function according to the basic principle.
Citation: Dongfang, X. D. Dongfang Special Entangled Schrödinger Wave Function of Hydrogen. Mathematics & Nature 3, 202304 (2023).
25. Dongfang Special Entangled Spherical Solution of Laplace Equation
The latest discovery of special entangled spherical harmonics indicates that traditional spherical harmonics are only a very narrow partial solution of spherical harmonic partial differential equations, and the theory of exact solutions for similar linear partial differential equations is therefore subject to disruptive effects. Here is a detailed introduction to the special entangled solution of the Laplace equation for the Dirichlet problem in a spherical region. Returning to the analytical form of the solution of spherical harmonic partial differential equations, it is first explained that in the special case where the magnetic quantum is zero, the spherical harmonic function partially degenerates into a Legendre function with respect to the angle θ, resulting in the existence of missing solutions in the Laplace equation. Then provide two special entangled solution sets for the Laplace equation with zero magnetic quantum number, including sine and cosine functions for angles θ and φ. The integral constant of the zero magnetic quantum number general solution in the special case formed by linear superposition of three types of special solution sets is not unique, indicating that the specific form of the exact solution of the Laplace equation cannot be determined. It can be seen that the conclusions of scientific theories described by partial differential equations are not absolutely reliable, and the theory of partial differential equations has serious flaws that urgently need to be improved.
Citation: Dongfang, X. D. Dongfang Special Entangled Spherical Solution of Laplace Equation. Mathematics & Nature 3, 202305 (2023).