By Zhong-Cheng Liang 1. Research purpose In this study, the spectral structure of hydrogen atom is analyzed according to the theory...

**By Zhong-Cheng Liang**

**1. Research purpose**

In this study, the spectral structure of hydrogen atom is analyzed according to the
theory of elastic particle motion. The aim is to provide a decisive argument for the
generality of elastic particle model and new quantum theory. From the motion
equilibrium equation, I derived the Balmer formula of atomic spectrum, predicted the
spectral frequency and the limit frequency, and clarified the relationship between the
spectral line-width and the transition time. The results show that the line spectrum
comes from the elastic vibration of atoms. The quantum state is the statistical
characteristics of elastic particle system, and quantum transition is the conversion
process between different motion modes of elastic particles.

**2. Physical inspiration**

The impact of billiards makes a sound, and the collision of atoms makes a light. This
analogy implies that both sound and light come from the vibration of elastic object,
and the difference lies in the vibration frequency and the human sensory organ.
Elastic object is three-dimensional body that has mass and volume, which can spin
and deform. Contemporary elastic theory regards elastic body as a continuous
medium, and studies the relationship between its stress and deformation. The
mathematics of dealing with continuous media is very complicated, because the
deformation of continuous media has infinite degrees of freedom. However, if we
regard an object as a discrete system composed of a finite number of elastic particles,
we can built a beautiful mathematical model for object with the method of classical
physics.

**3. Theoretical model**

It is known that inertia matrix (moment of inertia tensor) can be calculated for
classical particle systems. Therefore, the state of a particle system can be represented
by the inertia matrix. Furthermore, the motion of the particle system can be described
by the time variation of inertia matrix. The inertia matrix is a real symmetric matrix
with three real eigenvalues and three real eigenvectors, which respectively represent
the profile and posture of the particle system. In addition, the center of mass
represents the spatial position of the particle system. In the center-of-mass coordinate
frame, the time variations of profile, posture and position represent three independent
motion modes: vibration, rotation and translation. Each motion mode has three
degrees of freedom, and a particle system is simplified as an object of nine degrees of
freedom. If any object is regarded as a discrete system composed of N elastic
particles, then the object has 9N degrees of freedom. The state of an object is
expressed by the total energy {H, L,K} of the three motion modes. Then, we can
study the state changes in detail through a Cartesian energy space constructed by
{H, L,K}.

Figure 1. (a) Structure of energy space. (b) Equilibrium surfaces in energy space.

**4. Major discovery**

One of the important findings of elastic particle motion theory is to reveal the
classical statistical nature of quantum states. The averages of vibration energy,
rotation energy and translation energy of an object are
H v, L z, K T , respectively. As the scale (metric) of s = N
H = h s =
L
N = l s =
K
N = k
energy, {Hs
, Ls
,Ks} is the energy quantum. The quantum state is the state whose
digit (number) is integer {H, , on an equilibrium surface. According to this ˜ L˜ K˜ }
new quantum theory, I derived a modified Balmer formula of atomic spectrum in a
simple way. This formula makes a more reasonable explanation for the mechanism of
atomic radiation and gives a more detailed prediction for the characteristics of atomic
spectrum.

Figure 2. The plot of quantum state on equilibrium surface S [X] .

**5. Research story**

Ten years ago, I proposed a non-point-like particle model to explain the transport
mechanism of ionic liquids. In recent years, a systematic theory (real physics) is being
developed as an extension of this research. The core of real physics is to use elastic
particle model to replace the point-like particle of classical physics and the wave-like
particle of modern physics. This theory has made a fundamental revision to
contemporary physics, and its basic principles, concepts and conclusions are
revolutionary, so it is hard to be believed and understood by people. Real physics is
amazing in simplicity of principle, logical consistency and universal applicability. Its
successful application in unified field and phase transition convinced me that it is a
theory of everything. After a lonely but exciting exploration, I built an axiomatic
theoretical framework for real physics. The foundation of real physics is the statistics
of elastic particles. The buildings include the elastic particle field theory based on
mass and momentum statistics, the motion state theory based on energy statistics, and
the thermodynamic theory based on particle number statistics. The study of atomic
spectrum is a specific application of the motion state theory, and the purpose is to
demonstrate the universal applicability of real physics. Thanks to the editors,
reviewers and staff of the Global Journals, they recognize my research and provide
me with this publishing opportunity, communication platform and professional
support.

**About Author :**Dr. Zhong-Cheng Liang

**I graduated from the physics department of Nanjing Normal University in 1982 with a bachelor of science degree, and graduated from the physics department of the University of Science and Technology of China in 2001 with a doctor of science degree. I am currently working as a professor in the college of electronic and optical engineering of Nanjing University of Posts and Telecommunications. As a research scholar, I visited the physics department of Berlin Free University from September 1992 to February 1994, and the electronic engineering department of California Institute of Technology from September 2004 to February 2005. So far, I have published 2 monographs, authored and coauthored more than 200 journal articles in the fields of theoretical and experimental physics, electronic and optical engineering. My current research interest focuses on the fundamental issues of theoretical physics, such as the nature of particles, fields and interactions. The goal is to establish a systematic physical theory based on the model of elastic particles.**