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ABSTRACT
[align=justify]We ever investigated thousands of papers on solving Dirac equation published in many famous scientific journals and found that multitudinous and momentous mistakes of mathematical logics have been covered up by the corresponding specious explanations. Some papers seem to be purposive to make the inauthentic mathematical calculations and given the pseudo deductions for mixing the false with the genuine. Some papers seem to be unintentional to make the incorrect calculations but the ABC of differential equations such as existence of solution and uniqueness of solution and so on were missed. As examples, five typical literatures are criticized in the present paper. We disclose how the criticized literatures use many devious distortions to speciously fabricate the energy eigenvalues. These mistakes are covered up by the distinguished Dirac formula of the energy levels for hydrogen and hydrogen-like atoms. Most of such mistakes concealed in the criticized literatures are unable to be corrected. Fewness could be formally corrected but the corrected results are not in agreement with the order of nature.
1. Introduction
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Many incorrectly mathematical methods and logic relations have been used for solving the Dirac equation but have been covered up. Because of the specious explanations given in various literatures, the argumentations to the corresponding pseudo deductions were hardly understood. By some comments from many reviews of those famous journals, it was found that some basic problems of mathematics are missed. We sum up a kind of simple problems on solving Dirac equation with the pure Coulomb potential to formulate again those typical mistakes concealed in quantum mechanics. Because of the writing or involuntary techniques of composition, although such kind of the mathematics seem to be unconquerable, it is at least necessary to envisage those behaviors of coining physical law in quantum mechanics.
The soul of quantum mechanics is just deriving and solving the wave equation with the correct boundary condition or initial value condition. One cannot violate any basic mathematical rule to piece together any physical formula for being agreement with some experiment data. For nonrelativistic and relativistic quantum mechanics, once a wave equation is introduced and the initial value conditions or the natural boundary conditions are determined, all remnant physics should be essentially mathematics. When looking from a mathematical point of view, any of differential equations has the formal solution and the real solution respectively. From general solution, only the special solution that satisfies the uniqueness of solution and the boundary condition or the initial value condition does denote the real solution of the differential equations. However, in many literatureson Dirac’s relativistic quantum mechanics, these basic mathematical rules seem to be missed. It mainly behaves in two aspects. One is that the original Dirac equation of first order, by being introduced the real transformation of functions, were transformed into two second-order differential equations of second-order, which have two conflicting eigensolution sets, violating uniqueness of solution. Another is that some strange marks were introduced for constructing the so-called Schr鰀inger-like or Klein-Gordon-like equation, which conceals the breach of the uniqueness of solution and the boundary condition or coin solution. However, all of the corresponding mistakes were covered up by some specious explanations. Their main shelter is the distinguished Dirac solution for the hydrogen and hydrogen-like atom being recovered in form.
Here we criticize five examples of literatures chosen from thousands of the similar literatures. We focus on the obvious mathematical mistakes concealed in solving the Dirac equation with the Coulomb potential. Because Darwin and Gordon firstly gave the correct methods of finding the solution in 1928, one can easily judge the right and wrong of the criticized literatures. How the mathematical mistakes in those literatures take place, how the corresponding mathematical mistakes have been covered up, and those typical theories of coin on Dirac’s relativistic quantum mechanics were disclosed here.
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发表于 2008-2-23 16:50:40
