Doron Kwiat

One can represent quantum mechanics with real wave functions. The use of real wave functions leads to the interpretation of a single particle as consisting of two entities represented as coupled wave functions. Probability distributions are shown to be preserved for coupled wave functions just as for a single complex function. Assuming a string model [12-17], a double coupled string description is suggested, whereby the Schrödinger equation emerges naturally. This double-string description assumes a time-dependent tension [18] in the strings, together with a time-dependent interaction between the two strings. If the time pattern is similar for both tension and interaction, their ratio is shown to be ℏ/2. This leads to the derivation of Planck's constant as a result of strings interactions and characteristics.

]]>Walid Gewily

Since photon is the most common and abundant particle in our universe and a lot of its properties are under study, this research has done to investigate some of its properties by comparing the properties of the starting and final products in some annihilation processes; as a result some fundamental properties like structure, mass, length, velocity and motion path radius for photon have been deduced, and by relating these properties with the properties of other subatomic particles like proton, electron and positron; it was suggested that photon may be the origin of these subatomic particles, then the method of how these properties can be used for atomic radii calculation, explaining photoelectric effect, Compton effect and deriving some nature’s constants has been illustrated.

]]>Nura Yakubu, S. X. K. Huwusu, A. Adamu

The application of Newton’s laws of motion in gravitational fields has been restricted to the fields of perfectly spherical bodies. In this paper the gravitational fields due to a Spheroidal body is derived to open the way for the extension of Newtonian mechanics from the fields of spherical bodies to these Spheroidal bodies. The results showed that Newton’s gravitational field equations for a Spheroidal body are linear and separable and can be solved in terms of the well known special functions of mathematical physics, the Legendre functions. We also obtained gravitational intensity field of the body and its corresponding unit vectors in components forms. We further obtained general acceleration vector its associated acceleration vector components forms. We finally obtained the components of the equation of motion for a particle of non zero rest mass in the gravitational field exterior to an oblate spheroidal massive body. The Newton’s universal gravitational field equations for a homogeneous oblate Spheroidal body with the exact and complete results are available for mathematical analysis and hence physical interpretation and experimental investigation for all bodies in the universe.

]]>P. K. Chakraborty, B. N. Mondal

Exact quantum mechanical calculations of the Fermi-Integral (FI) associated with the density-of states (DOS) function for non-degenerately doped impurities in a parabolic band semiconductor were made. Unlike the results of previous approximate numerical calculations, present exact calculations showed novel oscillatory behavior of FI only for the positive values of the reduced Fermi-energies η (= E_{f}/k_{B}T), where E_{f }is the Fermi energy and k_{B} is the Boltzman constant and T is the absolute temperature. On the other hand, for the corresponding negative values, FI exhibited no oscillation. The observed non periodic oscillations were due to the Confluent Hypergeometric functional behavior of the presently derived expression of FI. Such oscillation might have massive effect on the dynamic behavior of quantum electronic properties of semiconductors as shown, for example, in case of Einstein relations (diffusivity-mobility ratio, DMR). Present finding also stimulate further investigation of DMR and similar other physical properties using the present exact expression of FI to explore the underlying new physics.

Franck Delplace

In this paper, we considered the laminar fully developed flow, of a Newtonian fluid, in ducts of rectangular cross-section. Poisson’s partial differential equation Saint-Venant solution was used, to calculate Poiseuille number values whatever is rectangles aspect ratio. From these results, we considered limit cases of square duct and plane Poiseuille flow (infinite parallel plates). We showed there exists a rectangle equivalent to a circular cross-section for energy dissipation through viscous friction. Finally, we gave some mathematical consequences of this approach for odd integers zeta function calculations and Catalan’s constant.

]]>Kunle Adegoke, Adenike Olatinwo, Olugbenga Olunloyo

In this note we show that the standard Rayleigh-Schrödinger (RS) perturbation method gives the same result as the hypervirial pertubative method (HPM), for an approximate analytic expression for the energy eigenvalues of the bounded quartic oscillator. This connection between the HPM and the RS method went unnoticed for a long time, apparently because it was not obvious that the resulting polygamma sums to be evaluated in the RS method could, in fact, be expressed in closed form.

]]>Godfrey E. Akpojotor, Omamoke O. E. Enaroseha, Alexander E. Animalu

We have shown in [1] that the geometric object for the geometrical and quantization foundation of the Oyibo grand unified theorem (GUT) is the torus. This torus is generic meaning that its nature depends on the periodic boundary conditions of the system and other physical constraint conditions. By observing that the Bloch’s theorem also has this torus as its generic geometric object, we show that there is correspondence between the Bloch’s theorem and the Oyibo GUT. The implication of this correspondence in using the Oyibo GUT to study strongly correlated systems in condensed mater physics is then discussed.

]]>Godfrey E. Akpojotor

Two fundamental arguments against the Oyibo grand unification theorem (GUT) as a possible mathematical basis for a grand unification theory are (1) the obscure nature of the unspecified “physical” or “geometrical” meaning of the group of transformation in Oyibo’s definition of conformal invariance and (2) the expectation that the yet-to-be resolved controversy on the possibility of quantizing the Einstein general theory of relativity (GTR) into a valid quantum theory of gravitation will be inherent in the Oyibo GUT. To resolve these arguments, it is demonstrated here that the torus can be used as an invariant geometrical object for the Oyibo GUT. It is also demonstrated that the Oyibo GUT can be created in N+1 dimensional background required for a theory of quantum gravity and that it can also be quantized as required for it to be adopted in the formulation of the quantum aspect of the Oyibo theory. The conclusion reached as in previous studies, is that the Oyibo GUT is a sound mathematical basis for a grand unified theory and therefore needs more attention of the scientific community.

]]>Ewa I. I., Lumbi L. W., Howusu S. X. K.

In this article, the golden Riemannian Laplacian operator was constructed using the golden metric tensor in spherical polar coordinate and was applied to the Schrodinger wave equation in order to obtain the golden Riemannian Schrodinger equation for a particle in a finite-potential well. The results are that the golden Riemannian Laplacian operator and golden Riemannian Schrodinger equation were augmented with additional correction terms; which are not found in the existing equations and can be applied to a finite-potential well problem, so as to obtain the expression for the allowed energy values.

]]>Vasil G. Angelov

The primary purpose of the present paper is to continue our studies from previous papers where the spin equations were derived. Here we prove an existence of a periodic solution of the spin equations system using fixed point method. As a consequence, we obtain that the general two-body problem of classical electrodynamics with radiation terms and spin is already solved.

]]>