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[align=justify]The first literature that we comment on is the book entitled “Anatomy on Choice Problems in Quantum Mechanics” [1] published by Science press, the first edition in 1988. For recovering the distinguished Dirac formula of the energy eigenvalues from the so-called second-order differential equation, in this book, a real transformation of functions was introduced. However the obtained two second-order equations have different formal eigenvalues sets, violating the uniqueness of solution. But one was chosen and another was stealthily deleted. The incorrect theory cannot be corrected.
The second literature that we comment on is the paper entitled ``Simplified solutions of the Dirac-Coulomb equation'' published by Physical Review in 1985 [2] constructed a new different system of first order differential equations with the strange hyperbolic functions, and it was called the radial Dirac-Coulomb equation. In fact, it is not the Dirac equation but is only a similar system of equations. In form, the new radial Dirac-like equations of first order were also transformed into the Schr鰀inger-like equation, in which four second-order differential equations were written in one form with another unnecessary sign {\\omega }=\\mp 1. By the correct mathematical calculation, we obtain two correct Schr鰀inger-like equations from the original Dirac-like equations without the unnecessary sign {\\omega }=\\mp 1, which are essentially different from the given form in the criticized paper, and solving the second-order equations violates the uniqueness of solution. One can only obtain the Dirac formula of energy eigenvalues by solving one of the second-order differential equations for the components of radial wave functions and hiding the other incompatible deduction of the energy eigenvalues from solving the other second-order differential equation. The theory cannot be corrected.
[align=justify]The third literature that we comment on is the paper entitled “A simpler solution of the Dirac equation in a Coulomb potential” [3] published by American Journal of Physics in 1997. There is a completely incorrect calculation of differential coefficient for the introduced new function with the matrix coefficients therein. All of deductions that come from this incorrect formula are hence completely incorrect. The corresponding comment on its pivotal mathematical mistakes ever incurred some traverses with the unreal mathematical calculations. In Fact, if we use the radial wave function given in the criticized paper to compare the other form that come from any real mathematical calculations, one will find how the unreal and incorrect mathematical calculation lead to specious deductions. None of the mistakes in this criticized paper can be corrected. |
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