paper

Historical pseudo simplified solution of the Dirac-Coulomb equation

arXiv:0707.0156

Abstract

One of the simplified solutions of the Dirac equations with the pure Coulomb potential given in a paper published in 1985 is pseudo. The original paper solved the Dirac equations by introducing a transformation of functions with two strange parameters a and b to transform the original system of the first-order differential equations into two uncoupled differential equations of second order. However, not only the given eigenvalues sets violate the uniqueness of solution but also the said second-order equations are not any necessarily mathematical deduction. In order to determine the introduced parameters, formally, the author actually introduced some self-contradictory mathematical formulas, such as sinh(theta)=2ab, cosh(theta)=a^2+b^2, tanh(theta)=-Z(alpha)/k, a^2-b^2=1, b=sinh((theta/2), a=cosh((theta/2). But one has not known the value of the parameters a and b all the while, whereas the parameters were insensibly deleted in the given second-order Dirac-Coulomb equation last. One cannot recover any result given in the paper by making corresponding correctly mathematical calculations.

10 pages, no figure, 35 equations. The v1 version entitled "A hidden incorrect solution of second-order Dirac-Coulomb equation with a direct transformation of functions" has been withdrawn by the author due to a crucial mathematics error in equations 20

References in corpus (5)

Cited by in corpus (1)