[9] **viXra:1708.0198 [pdf]**
*submitted on 2017-08-17 01:42:13*

**Authors:** Vu B Ho

**Comments:** 24 Pages.

In this work we discuss the possibility of reconciling quantum mechanics with classical mechanics by formulating a temporal dynamics, which is a dynamics caused by the rate of change of time with respect to distance. First, we show that a temporal dynamics can be derived from the time dilation formula in Einstein’s theory of special relativity. Then we show that a short-lived time-dependent force derived from a dynamical equation that is obtained from the temporal dynamics in a 1-dimensional temporal manifold can be used to describe Bohr’s postulates of quantum radiation and quantum transition between stable orbits in terms of classical dynamics and differential geometry. We extend our discussions on formulating a temporal dynamics to a 3-dimensional temporal manifold. With this generalisation we are able to demonstrate that a sub-quantum dynamics is a classical dynamics.

**Category:** Mathematical Physics

[8] **viXra:1708.0197 [pdf]**
*submitted on 2017-08-17 01:50:44*

**Authors:** Vu B Ho

**Comments:** 10 Pages.

In this work we discuss the possibility of combining the Coulomb potential with the Yukawa’s potential to form a mixed potential and then investigate whether this combination can be used to explain why the electron does not radiate when it manifests in the form of circular motions around the nucleus. We show that the mixed Coulomb-Yukawa potential can yield stationary orbits with zero net force, therefore if the electron moves around the nucleus in these orbits it will not radiate according to classical electrodynamics. We also show that in these stationary orbits, the kinetic energy of the electron is converted into potential energy, therefore the radiation process of a hydrogen-like atom does not related to the transition of the electron as a classical particle between the energy levels. The radial distribution functions of the wave equation determine the energy density rather than the electron density at a distance r along a given direction from the nucleus. It is shown in the appendix that the mixed potential used in this work can be derived from Einstein’s general theory of relativity by choosing a suitable energy-momentum tensor. Even though such derivation is not essential in our discussions, it shows that there is a possible connection between general relativity and quantum physics at the quantum level.

**Category:** Mathematical Physics

[7] **viXra:1708.0196 [pdf]**
*submitted on 2017-08-17 01:54:09*

**Authors:** Vu B Ho

**Comments:** 15 Pages.

In this work we develop a theory of temporal relativity, which includes a temporal special relativity and a temporal general relativity, on the basis of a generalised Newtonian temporal dynamics. We then show that a temporal relativity can be used to study the dynamics of quantum radiation of an elementary particle from a quantum system.

**Category:** Mathematical Physics

[6] **viXra:1708.0192 [pdf]**
*submitted on 2017-08-17 03:51:07*

**Authors:** Vu B Ho

**Comments:** 18 Pages.

In this work we propose a covariant formulation for the gravitational field and derive equations that can be used to construct the spacetime structures for short-lived and stable quantum particles. We also show that Schrödinger wavefunctions can be used to construct spacetime structures for the quantum states of a quantum system, such as the hydrogen atom. Even though our discussions in this work are focused on the microscopic objects, the results obtained can be applied equally to the macroscopic phenomena.

**Category:** Mathematical Physics

[5] **viXra:1708.0184 [pdf]**
*submitted on 2017-08-16 10:47:23*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 10 Pages.

In a previous work I have derived the theory of everything (ToE) in a 74 pages paper. To make the theory more accessible, in this work, I derive the equation for the ToE on one page. I then follow the derivation with a few pages of discussion.

**Category:** Mathematical Physics

[4] **viXra:1708.0166 [pdf]**
*submitted on 2017-08-15 06:49:15*

**Authors:** Spiros Konstantogiannis

**Comments:** 50 Pages.

Exactly solvable rational extensions of the harmonic oscillator have been constructed as supersymmetric partner potentials of the harmonic oscillator [1] as well as using the so-called prepotential approach [2]. In this work, we use the factorization property of the energy eigenfunctions of the harmonic oscillator and a simple integrability condition to construct and examine series of regular and singular rational extensions of the harmonic oscillator with two known eigenstates, one of which is the ground state. Special emphasis is given to the interrelation between the special zeros of the wave function, the poles of the potential, and the excitation of the non-ground state. In the last section, we analyze specific examples.

**Category:** Mathematical Physics

[3] **viXra:1708.0147 [pdf]**
*submitted on 2017-08-13 21:51:40*

**Authors:** Harry Watson

**Comments:** 1 Page.

Abstract: Consider the product
(4pi)(4pi-1/pi)(4pi-2/pi)(pi-2/pi)(4pi-4/pi).
The product of the first three terms is 1836.15.
The product of the last two terms is 134.72. The mass ratio of the proton to the electron is 1836.15.
We may sharpen the result by letting the last two terms be (4pi-3/pi)(4pi-4/pi) = 131.13$.

**Category:** Mathematical Physics

[2] **viXra:1708.0031 [pdf]**
*replaced on 2017-08-04 07:06:47*

**Authors:** Hideki Mutoh

**Comments:** 5 Pages.

Dirac equation includes the 4 x 4 complex differential operator matrix, which is one of square roots of d' Alembertian with spin. We found another 4 x 4 complex differential matrix as a spinless square root of d' Alembertian, which we call diamond operator. The extended Maxwell's equations including charge creation-annihilation field and the linear gravitational field equations including energy creation-annihilation field can be simply written by using the diamond operator. It is shown that the linear gravitational field equations derive Klein-Gordon equation, time independent Schrödinger equation, and the principle of quantum mechanics.

**Category:** Mathematical Physics

[1] **viXra:1708.0011 [pdf]**
*submitted on 2017-08-02 04:28:15*

**Authors:** Hong Lai Zhu

**Comments:** 53 Pages.

In this paper, using proposed three new transformation methods we have solved general solutions and exact solutions of the problems of definite solutions of the Laplace equation, Poisson equation, Schrödinger equation, the homogeneous and non-homogeneous wave equations, Helmholtz equation and heat equation. In the process of solving, we find that in the more general case, general solutions of partial differential equations have various forms such as basic general solution, series general solution, transformational general solution, generalized series general solution and so on.

**Category:** Mathematical Physics