arXiv subjects

Ruida Chen

Publications and source records attributed to Ruida Chen.

4 recordsLinked to original sources

arXiv2007

Historical pseudo simplified solution of the Dirac-Coulomb equation

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.

physics.gen-ph↗

arXiv2007

Unheeded pseudo solution of Dirac-Coulomb equations with an indirect transformation of functions

We open out one of incorrect solutions of the Driac equation in the Coulomb field given in a published paper. By introducing a transformation of function, the paper transformed the original radial first-order Dirac-Coulomb equation into two second-order Dirac-Coulomb equation. However, each of the second-order differential equations has differential energy eigenvalues set. The original paper wrote the two differential equations into one of forms, and then gave the distinguished energy eigenvalues. The mathematical procedure is not correct. For the same quantum system, introducing a transformation of function yields two different energy eigenvaluse, the result violates the uniqueness of solution. It actually shows that the given second-order differential equations have no solution. On the other hand, the given formal solutions of the second-order Dirac-Coulomb equations violate the conditions for determining solution. Consequently, the solutions given by the author are pseudo solution, and the corresponding energy eigenvalues set is also a pseudo eigenvalues set.

physics.gen-ph↗

arXiv2007

Established pseudo solution of second-order Dirac-Coulomb equation with position-dependent mass

We show that one of exact solutions of the second-order Dirac-Coulomb equation were pseudo. In the corresponding original literature, it was considered that the mass of the electron with a Coulomb potential was position-dependent, but the obtained eigenvalues set was not the inevitable mathematical deduction of the given second-order Dirac equation, and the second-order Dirac equations were not the inevitable mathematical deduction of the given couplet first-order Dirac equation with the position-dependent mass of the electron. In the present paper, we obtain the correct solution of the introduced first-order differential equations. This new solution would be tenable only when the wave equation is correct, but there is not any experiment date to validate the so-called position-dependent of the electron in the Coulomb field.

physics.gen-ph↗

arXiv2007

New exact solution of Dirac-Coulomb equation with exact boundary condition

It usually writes the boundary condition of the wave equation in the Coulomb field as a rough form without considering the size of the atomic nucleus. The rough expression brings on that the solutions of the Klein-Gordon equation and the Dirac equation with the Coulomb potential are divergent at the origin of the coordinates, also the virtual energies, when the nuclear charges number Z > 137, meaning the original solutions do not satisfy the conditions for determining solution. Any divergences of the wave functions also imply that the probability density of the meson or the electron would rapidly increase when they are closing to the atomic nucleus. What it predicts is not a truth that the atom in ground state would rapidly collapse to the neutron-like. We consider that the atomic nucleus has definite radius and write the exact boundary condition for the hydrogen and hydrogen-like atom, then newly solve the radial Dirac-Coulomb equation and obtain a new exact solution without any mathematical and physical difficulties. Unexpectedly, the K value constructed by Dirac is naturally written in the barrier width or the equivalent radius of the atomic nucleus in solving the Dirac equation with the exact boundary condition, and it is independent of the quantum energy. Without any divergent wave function and the virtual energies, we obtain a new formula of the energy levels that is different from the Dirac formula of the energy levels in the Coulomb field.

quant-ph↗