G-Function Solutions for Schrodinger Equation in Cylindrical Coordinates System

In this paper, the Schr?dinger equation is solved by Modified separation of variables (MSV) method suggested by Pishkoo and Darus. Using this method, Meijer’s G-function solutions are derived in cylindrical coordinate system for quantum particle in cylindrical can. All elementary functions and most of the special functions which are the solution of extensive problems in physics and engineering are special cases of Meijer’s G-functions.

一类Schrdinger方程混合问题解的H^s(Ω)有界性

研究一类高维空间中Schr dinger方程混合问题解在Hs(Ω)中的有界性 ,其结果在研究整体解时是非常重要的 .

Tiêu Equation Experimentation of Understanding by Energy Transfer Quantum Mechanics

Background: The Tiêu equation has a ground roots approach to the process of Quantum Biology and goes deeper through the incorporation of Quantum Mechanics. The process can be measured in plant, animal, and human usage through a variety of experimental or testing forms. Animal studies were conducted for which, in the first day of the study all the animals consistently gained dramatic weight, even as a toxic substance was introduced as described in the introduction of the paper to harm animal subjects which induced weight loss through toxicity. Tests can be made by incorporating blood report results. Human patients were also observed to show improvement to their health as administration of the substance was introduced to the biological mechanism and plants were initially exposed to the substance to observe results. This is consistent with the Tiêu equation which provides that wave function is created as the introduction of the substance to the biological mechanism which supports Quantum Mechanics. The Tiêu equation demonstrates that Quantum Mechanics moves a particle by temperature producing energy thru the blood-brain barrier for example. Methods: The methods for the Tiêu equation incorporate animal studies to include the substance administered through laboratory standards using Good Laboratory Practices under Title 40 C.F.R. § 158. Human patients were treated with the substance by medical professionals who are experts in their field and have knowledge to the response of patients. Plant applications were acquired for observation and guidance of ongoing experiments of animals’ representative for the biologics mechanism. Results: The animal studies along with patient blood testing results have been an impressive line that has followed the Tiêu equation to consistently show improvement in the introduction of the innovation to biologic mechanisms. The mechanism responds to the substance by producing energy to the mechanism with efficient effect. For plant observations, plant organisms responded, and were seen as showing improvement thru visual observation.

Dirichlet-to-Neumann Map for a Hyperbolic Equation

In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for a hyperbolic differential equation in 3-dimensional. We show that the Dirichlet-Neumann operators corresponding to a potential radial have the same properties for hyperbolic differential equations as for elliptic differential equations. We numerically implement the coefficients of the explicit formulas. Moreover, a Lipschitz type stability is established near the edge of the domain by an estimation constant. That is necessary for the reconstruction of the potential from Dirichlet-to-Neumann map in the inverse problem for a hyperbolic differential equation.

Review of Feynman’s Path Integral in Quantum Statistics:from the Molecular Schrödinger Equation to Kleinert’s Variational Perturbation Theory

Feynman’s path integral reformulates the quantum Schrödinger differential equation to be an integral equation.It has been being widely used to compute internuclear quantum-statistical effects on many-body molecular systems.In this Review,the molecular Schrödinger equation will first be introduced,together with the BornOppenheimer approximation that decouples electronic and internuclear motions.Some effective semiclassical potentials,e.g.,centroid potential,which are all formulated in terms of Feynman’s path integral,will be discussed and compared.These semiclassical potentials can be used to directly calculate the quantum canonical partition function without individual Schrödinger’s energy eigenvalues.As a result,path integrations are conventionally performed with Monte Carlo and molecular dynamics sampling techniques.To complement these techniques,we will examine how Kleinert’s variational perturbation(KP)theory can provide a complete theoretical foundation for developing non-sampling/non-stochastic methods to systematically calculate centroid potential.To enable the powerful KP theory to be practical for many-body molecular systems,we have proposed a new path-integral method:automated integrationfree path-integral(AIF-PI)method.Due to the integration-free and computationally inexpensive characteristics of our AIF-PI method,we have used it to perform ab initio path-integral calculations of kinetic isotope effects on proton-transfer and RNA-related phosphoryl-transfer chemical reactions.The computational procedure of using our AIF-PI method,along with the features of our new centroid path-integral theory at the minimum of the absolute-zero energy(AMAZE),are also highlighted in this review.

Hirota双线性导数变换与DNLS方程的孤子解

介绍并基于Hirota双线性导数变换，零边值条件下DNLS方程得以直接求解．其单孤子与双孤子解被作为两个典型特例以说明双线性导数变换法的一般应用手续．孤子之间的弹性碰撞通过双孤子情形得以展示，单孤子和双孤子解随时间与空间的演化也通过图表加以演示．

Theoretical Evidence for Wave Nature of Micro Particle and New Theory of Its Collective Motion in Material

Since a material is composed of micro particles, investigating behavior of those particles is essentially dominant for materials science. The diffusivity of diffusion equation is relevant to not only a collective motion of micro particles but also a motion of single particle. An elementary process of diffusion was thus theoretically investigated in a local space and time. As a result, the investigation concluded that the wave nature of micro particle results from denying the mathematical density theorem of a real time in the Newton mechanics. In other words, the basic theory of quantum mechanics is established in accordance with the cause-and-effect relationship in the Newton mechanics, for the first time, regardless of the de Broglie hypothesis. In relation to the collective motion of micro particles, the new diffusion theory was also reasonably established using the universal expression of diffusivity obtained here. In the present paper, the new findings indispensable for the fundamental knowledge in physics are thus systematically discussed in accordance with the theoretical frame in physics.

Conceptual Problems in Bell’s Inequality and Quantum Entanglement

The description of the microscopic world in quantum mechanics is very different from that in classical physics, and there are some points of view that are contrary to intuition and logic. The first is the problem of reality;quantum mechanics believes the behavior of micro particles is random and jumping. The second is the loss of certainty;the conjugate physical variables of a system cannot be determined synchronously, they satisfy the Heisenberg uncertainty principle. The third is the non-local correlation. The measurement of one particle in the quantum entanglement pair will influence the state of the other entangled particle simultaneously. In this paper, some concepts related to quantum entanglement, such as EPR correlation, quantum entanglement correlation function, Bell’s inequality and so on, are analyzed in detail. Analysis shows that the mystery and confusion in quantum theory may be caused by the logical problems in its basic framework. Bell’s inequality is only a mathematical theorem, but its physical meaning is actually unclear. The Bell state of quantum entangled pair may not satisfy the dynamic equation of quantum theory, so it cannot describe the true state of microscopic particles. In this paper, the correct correlation functions of spin entanglement pair and photonic entanglement pair are strictly derived according to normal logic. Quantum theory is a more fundamental theory than classical mechanics, and they are not equal relation in logic. However, there are still some unreasonable contents in the framework of quantum theory, which need to be improved. In order to disclose the real relationship between quantum theory and classical mechanics, we propose some experiments which provide intuitionistic teaching materials for the new interpretation of quantum theory.

How Quantum Mechanics and General Relativity Can Be Brought Together

This paper describes an easy and teaching way how quantum mechanics (QM) and general relativity (GR) can be brought together. The method consists of formulating Schrödinger’s equation of a free quantum wave of a massive particle in curved space-time of GR using the Schwarzschild metric. The result is a Schrödinger equation of the particle which is automatically subjected to Newtons’s gravitational potential.

Dynamics of the Spherical Charged Clots

In work, dynamics of the spherical loaded clots is studied. For the self-coordinated description of non-stationary processes model representation of potential, obviously time-dependent and allowing construction movement integral is used. Classical and quantum tasks are considered.