MATHEMATICS & NATURE
Mathematics,Physics, Mechanics & Astronomy
Random Vol. 2 Sn: 202204
https://mathnature.github.io
c
⃝ Mathematics & Nature–Free Media of Eternal Truth, China, 2022 https://orcid.org/0000-0002-3644-5170
.
Article
.
Mathematics and Physics
The End of Isomeric Second Order Dirac Hydrogen Equations
X. D. Dongfang
Orient Research Base of Mathematics and Physics,
Wutong Mountain National Forest Park, Shenzhen, China
Biedenharn and Wong wrote the Dirac equation in the form that the combination of the differential
term and the function term is equal to zero, then changed the positive and negative sign of the mass
term and removed the wave function to extract a mixing operator, and then used this mixing operator
to act on the first-order Dirac equation. The resulting second-order equation is called the isomeric
second-order Dirac equation. Because the equations in mathematical sense can be constructed arbi-
trarily, the isomeric second-order Dirac equation can exist as a pure differential equation. However, as
the wave equation of quantum mechanics, the isomeric second-order Dirac equation advocated by fa-
mous journals seriously lacks scientific basis and destroys mathematical principles, and the processing
of isomeric second-order Dirac equation is completely false calculation. Here, the real heterogeneous
second-order Dirac equation is first derived, and it is proved that it is a system of equations composed
of four non-solvable second-order partial differential equations of four wave function components.
Then it is proved that the highly respected second-order Dirac equation of single-comp onent wave
function isomerism is forged, and the Dirac energy level formula of hydrogen atom pieced together is
only a prop to cover up the above lies. Then it is proved that the most ideal isomeric second-order
radial Dirac equation of hydrogen atom is also an unsolvable differential equation system composed of
at least two partial differential equations, which further illustrates the fraud of the highly respected
isomeric second-order Dirac equation of single-component wave function. Finally, it is proved that
the mixed operator method for constructing the isomeric second-order Dirac equation destroys the
unitary principle and leads to many confused and uncertain conclusions. The results of these rigorous
calculations declare the end of the heterogeneous second-order Dirac equation and the mixed operator
metho d itself used for the construction of heterogeneous wave equations.
Keywords: Dirac equation; Isomeric equation; Mixing operator; Spurious calculation; Spurious
equation; Unsolvability.
PACS number(s): 03.65.Pm—Relativistic wave equations; 03.65.Ge—Solutions of wave equations:
b ound states; 32.10.Fn—Fine and hyperfine structure; 33.15.Pw—Fine and hyperfine structure.
1 Introduction
The great influence of the Dirac equation
[1-7]
has led
to the emergence of various named Dirac equations. The
teratogenic simplified second order Dirac hydrogen equa-
tion has been terminated
[8]
because it actually has two
contradictory solutions, one that meets the exp ectation
and the other that does not meet the expectation. The
solution that does not meet the expectation has been
deleted by the excuse of decoupling, and the expected
solution is retained. Even so, the reader can check that
the expected solution of the reserved second order equa-
tion does not actually meet the corresponding first-order
equations. To millions of articles of Dirac equation, we
only need to test the wave function called the solution
of the equation into the equation, and we will know that
many calculations are not true. I call such untrue calcu-
lations false calculations.
As the development theory of the Dirac equation, the
teratogenic equation makes us doubt the credibility of
the praise of the Dirac equation expressed by the scien-
tific community. Praise of modern physics often stays in
the description of philosophical significance and evades
the logical argument. For example, Dirac equation leads
to the strange Dirac Sea
[9]
, Dirac equation predicts the
existence of antimatter
[10]
, and Dirac equation natural-
ly describes the spin of particles
[11]
. However, Dirac e-
quation has no causal relationship with so many events,
but it is described as an inevitable causal law. As a
part of the Dirac equation, Dirac matrix
[12, 13]
is usually
bound with the Pauli matrix
[14]
. In fact, Dirac matrix
is at least a fourth order matrix, while Pauli matrix is
a second order matrix. When we combine the two to
transform the Dirac equation of the fourth order ma-
trix into the Dirac equation of the second order matrix,
we should prove that there is an inevitable causal rela-
tionship between the Dirac fourth order matrix and the
Pauli second order matrix, rather than blindly praising
it. What is the actual situation? Too much praise of
philosophical significance led physicists to focus on the
)Citation: Dongfang, X. D. The End of Isomeric Second Order Dirac Hydrogen Equations. Mathematics & Nature 2, 202204 (2022).
202204-2 X. D. Dongfang The End of Isomeric Second Order Dirac Hydrogen Equations
cloning and interpretation of the highly praised theory
and gave up the important process of scientific research
such as conclusion and logical test imperceptibly.
Mathematics is the precise language of physics. But
there are still great differences between the mathemat-
ical language of physics and pure mathematics. Pure
mathematics can write an equation at will to discuss
the solution of the equation, but physics cannot write
an equation at will. Physical equations such as wave e-
quations must be based on basic physical laws such as
Newton’s laws of motion. The solution of the differen-
tial equation in a pure mathematical sense only needs to
satisfy the differential equation and the definite solution
condition, while the solution of the physical differential
equation only satisfying the differential equation and the
definite solution condition is often not enough. This is
because the definite solution condition is not necessarily
unique. If the definite solution condition is not appropri-
ate, the resulting solution may be a false solution. Some
examples have been listed before. Pseudo solutions of-
ten hide irreconcilable logical contradictions. Although
the pseudo solutions of wave equations often meet expec-
tations after processing, it is the result of unreasonable
calculation.
From a purely mathematical point of view, Dirac e-
quation is really attractive. Its construction method is
ingenious, and the equation processing hides variabili-
ty, which will greatly enrich the content of mathematics.
However, as a physical equation, the scientific basis of
equation construction, the inevitable causal relationship
between the result and the basic laws of physics, and
the uniqueness of the solution of the equation need to
be treated again with enough patience. Dirac equation
gave birth to a large number of flashy equations. Here
we discuss the isomeric second-order Dirac equation. Its
construction process is to first move the function term in
the original Dirac equation to one side, remove the wave
function and get a mixing operator, then change the
positive and negative sign of the quality in the mixing
operator to construct a heteromorphic mixing operator,
and then multiply the heteromorphic mixing operator by
the original mixing operator, and the result acts on the
wave function, claiming that the obtained second-order
equation is a second-order Dirac equation. This paper
proves that the isomeric second-order Dirac equation,
which is highly praised by famous journals, is the result
of false calculation and the so-called exact solution is on-
ly patchwork. Then the real isomeric second-order Dirac
equation is given, and it is proved that the real isomer-
ic second-order Dirac hydrogen equation is not solvable.
Thus, the isomeric second-order Dirac equation and the
isomeric method itself were also declared to be over.
2 Conclusions and comments
The theory of isomeric second-order Dirac equation
advocated by famous journals is completely wrong. It
does not really develop the theory of Dirac quantum
mechanics. The founder of the theory seems to lack the
applied mathematical foundation and necessary scientif-
ic logic. Instead, he made up a false theory that could
not pass the calculation test by stating the false memory
and quoting the celebrity equation without causal rela-
tionship, listing the false calculations and writing the
so-called second-order Dirac equation of the single com-
ponent wave function that did not exist in fact. The
actual effect just exposed the hypocrisy and fraud of
the peer review system. From a mathematical point of
view, I give the real deduction of the isomeric second-
order Dirac equation from the mixed Dirac operator,
and the result is the second-order partial differential e-
quation of the four wave function components that can-
not be solved. It is further proved that the formula of
Dirac energy level given by the isomeric second-order
Dirac equation is a lie. The insolubility of the ideal
hydrogen atom isomeric second-order radial Dirac equa-
tion declares the complete end of the theory of isomeric
second-order Dirac equation. The construction of wave
equations by mixed operators leads to the uncertainty of
results, and the construction of wave equations by mixed
operators leads to the confusion of physical conclusions,
which is destructive to the unitary principle and declares
the end of the method of constructing wave equations by
mixed operators.
The end of the theory of isomeric second-order Dirac
equation has cleared another obstacle for the correct un-
derstanding of Dirac electron theory. At the same time,
the author reiterated the view expressed by studying the
evolution of the angular motion law operator
[]
: the ap-
plication scope of the quantum mechanics principle of
constructing wave equations by operators is very lim-
ited, and the operators only act on the wave function,
not the potential function and other functions. Some
thorny problems in the processing of wave equations in
quantum mechanics caused by this need to be consid-
ered from multiple perspectives, and the processing re-
sults conforming to the unitary principle are relatively
reliable. Science has strict logic. Theoretical physics
should draw conclusions from correct calculations. Cog-
nitive errors or computational errors can be corrected
eventually. When trying to establish a new physical the-
ory, we should give up the establishment of the theory
when we can’t calculate, instead of avoiding calculation,
focus on quoting the celebrity equation without causali-
ty that we have never read and tested, vividly describe
personal fantasy, fabricate false logic, and create the il-
lusion of scientific inference. Some theories, conclusions
and experimental reports of modern physics are fabricat-
ed in this way and cannot pass the strict test of Dong-
fang’s unitary principle. Some famous academic journals
Mathematics & Nature (2022) Vol. 2 No. 1 202204-3
flaunt academic ethics, but they have always tried to de-
fend academic lies, strangle, slander and even plagiarize
those groundbreaking and correct scientific discoveries.
The experience of communication with scientific jour-
nals in the past 40 years has proved that many famous
journals do not really care about new scientific discov-
eries but pay more attention to safeguarding the fame
and interests of interest groups and individuals. The
groundbreaking and great discoveries made by the bot-
tom scientists can and can only be spread to the world
with the lowest efficiency by means similar to leaflets.
To foretell a new conclusion that needs strong log-
ic support: Dirac equation is not the ultimate answer
to quantum mechanics, and its position in physics may
gradually decline with the passage of time. However, the
Dirac equation construction method is one of the most
attractive methods for constructing partial differential
equations. The Dirac equation will bring rich and color-
ful mathematical problems, which will gradually increase
its position in mathematics. It is by no means easy to
construct a truly scientific and widely applicable wave
equation that can correctly describe the laws of nature.
Construction of wave equation needs the support of ba-
sic laws of physics and mathematical principles. The
wave equation that conforms to the unitary principle
in a wider range derived from the basic laws of physics
and mathematical principles will be the ultimate answer.
Some wave equations constructed by the operator princi-
ple of quantum mechanics, such as Schr¨odinger equation,
Klein-Gordon equation and the Dirac equation, may on-
ly be transitional equations of quantum theory. We need
a unified quantum theory that conforms to the unitary
principle from the field of mathematics to the field of
physics, which is suitable for describing both macroscop-
ic and microscopic laws of motion.
1 Dirac, P. A. M. The quantum theory of the electron. Part
II. Proceedings of the Royal Society of London. Series A,
Containing Papers of a Mathematical and Physical Charac-
ter 118, 351-361 (1928).
2 Dirac, P. A. M. The principles of quantum mechanics. (Ox-
ford university press, 1981).
3 Thaller, B. The dirac equation. (Springer Science & Business
Media, 2013).
4 Greiner, W. Relativistic quantum mechanics. Vol. 2
(Springer, 2000).
5 Schiff, L. I. Quantum Mechanics 3rd. New York: M cGraw-
Hill (1968).
6 Zeng, J. Y. Quantum Mechanics II. 611-620 (Beijing: Science
Press, 1997).
7 Dongfang, X. The End of Teratogenic Simplified Dirac Hy-
drogen Equations. Mathematics & Nature 2, 012 (2022).
8 Dongfang, X. The End of Teratogenic Simplified Dirac Hy-
drogen Equations. Mathematics & Nature 2, 012 (2022).
9 Dirac, P. A. M. A theory of electrons and protons. Proceed-
ings of the Royal Society of London. Series A, Containing
papers of a mathematical and physical character 126, 360-
365 (1930).
10 Dirac, P. A. M. The quantum theory of the electron. Proceed-
ings of the Royal Society of London. Series A, Containing
Papers of a Mathematical and Physical Character 117, 610-
624 (1928).
11 Hestenes, D. Real spinor fields. Journal of Mathematical
Physics 8, 798-808 (1967).
12 Good Jr, R. Properties of the Dirac matrices. Reviews of
Modern Physics 27, 187 (1955).
13 Macfarlane, A. Dirac matrices and the Dirac matrix descrip-
tion of Lorentz transformations. Communications in Mathe-
matical Physics 2, 133-146 (1966).
14 Patera, J. & Zassenhaus, H. The Pauli matrices in n dimen-
sions and finest gradings of simple Lie algebras of type A n-
1. Journal of mathematical physics 29, 665-673 (1988).
15 Biedenharn, L. C. Remarks on the relativistic Kepler prob-
lem. Physical Review 126, 845 (1962).
16 Biedenharn, L., Han, M. & Van Dam, H. Two-component
alternative to Dirac’s equation. Physical Review D 6, 500
(1972).
17 Wong, M. & Yeh, H.-Y. Simplified solution of the Dirac e-
quation with a Coulomb p otential. Physical Review D 25,
3396 (1982).
18 Wong, M. & Yeh, H.-Y. Exact solution of the Dirac-Coulomb
equation and its application to bound-state problems. I Ex-
ternal fields. Physical Review A 27, 2300 (1983).
19 Wong, M. & Yeh, H.-Y. Exact solution of the Dirac-Coulomb
equation and its application to bound-state problems. II. In-
teraction with radiation. Physical Review A 27, 2305 (1983).
20 Dongfang, X. D. On the relativity of the speed of light. Math-
ematics & Nature 1, 202101 (2021).
21 Dongfang, X. D. The Morbid Equation of Quantum Numbers.
Mathematics & Nature 1, 202102 (2021).
22 Dongfang, X. D. Relativistic Equation Failure for LIGO Sig-
nals. Mathematics & Nature 1, 202103 (2021).
23 Dongfang, X. D. Dongfang Com Quantum Equations for
LIGO Signal. Mathematics & Nature 1, 202106 (2021).
24 Dongfang, X. D. Com Quantum Proof of LIGO Binary Merg-
ers Failure. Mathematics & Nature 1, 202107 (2021).
25 Dongfang, X. D. Dongfang Modified Equations of Molecular
Dynamics. Mathematics & Nature 1, 202104 (2021).
26 Dongfang, X. D. Dongfang Angular Motion Law and Opera-
tor Equations. Mathematics & Nature 1, 202105 (2021).
27 Dongfang, X. D. Dongfang Modified Equations of Electro-
magnetic Wave. Mathematics & Nature 1, 202108 (2021).
28 Dongfang, X. D. Nuclear Force Constants Mapped by Yukawa
Potential. Mathematics & Nature 1, 202109 (2021).
29 Dongfang, X. D. The End of Yukawa Meson Theory of Nu-
clear Forces. Mathematics & Nature 1, 202110(2021).
30 Dongfang, X. D. The End of Klein-Gordon Equation for
Coulomb Field. Mathematics & Nature 2, 202201 (2022).
31 Dongfang, X. D. The End of Teratogenic Simplified Dirac Hy-
drogen Equations. Mathematics & Nature 2, 202202 (2022).
32 Dongfang, X. D. Dongfang Solution of Induced Second Order
Dirac Equations. Mathematics & Nature 2, 202203 (2022).
Latest findings
The End of True Second Order Dirac Hydrogen Equation
The original Coulomb field radial Dirac equation is essentially a first order differential system of two-component wave functions. The second order differential equation of the original wave function component directly converted from the first order differential equation set is called the true second order Dirac equation. Relativistic quantum mechanics usually ignores the physical meaning of wave function and only focuses on the energy eigenvalue. So, the main expectation of solving the true second order Dirac equation of hydrogen-like atoms is that the Dirac energy level formula is the eigenvalue of the equation. Here I derive two true second order Dirac equations that are mutually independent in form but actually constrained by common energy parameters, and then use the traditional boundary conditions of hydrogen-like atoms to solve the true second order Dirac equation. The conclusion drawn from this is not exactly the same as the traditional understanding. 1) The formal solution of the true second order Dirac equation satisfying the traditional boundary conditions takes the Dirac hydrogen level formula as the energy eigensolution, which seems to meet the expectation; 2) However, when the radial quantum number is 0, regardless of the value of the angular quantum number, the complete expression of the wave function as the exact solution of the equation diverges at the coordinate origin, which does not meet the traditional boundary conditions, which means that the universe is collapsed and does not conform to the fact of the universe structure. From this it is concluded that the Dirac energy level formula is only the formal eigenvalue of the true second order Dirac equation that does not conform to the physical meaning. This announced the end of the expectation of using traditional boundary conditions to solve the true second order Dirac equation to naturally obtain the Dirac energy level formula. This result will promote the re-study of the exact solution of the original Dirac equation.