Arbitrary Solution of the Schrödinger Equation Interacting with the Superposition of Hulthen with Spin-orbit Plus Adjusted Coulomb Potential Model

In this study, we solve the non-relativistic radial part of the Schrödinger wave equation for the superposition of the Hulthen with spin-orbit plus adjusted Coulomb potential (SHSC) potential using the Nikiforov-Uvarov (NU) method for arbitrary states. The Hulthen with spin-orbit plus adjusted Coulomb (SHSC) potential is the simplest potential field for a nuclear system and has been used to obtain the single particle energy spectrum for both nucleon species orbiting a closed nuclear core. We also obtained in this study the corresponding single particle normalized wave function expressed in terms of the Jacobi polynomial. Besides, we obtained two special cases of the energy spectra for the SHSC potential.

The Schrödinger Equation with Deng-Fan-Eckart Potential (DFEP): Nikiforov-Uvarov-Functional Analysis (NUFA) Method

In this study, the radial part of the Schrödinger equation with the Deng-Fan-Eckart potential (DFEP) is solved analytically by employing the improved Greene and Aldrich approximation to bypass the centrifugal barrier and using the Nikiforov-Uvarov-Functional Analysis method (NUFA). The energy expression and wave function are obtained respectively. The numerical energy spectra for some diatomic molecules have been studied and compared with the findings of earlier studies and it has been found to be in good agreement. The NUFA method used in this study is easy and very less cumbersome compared to other methods that currently exist and it is recommended that researchers in this area adopt this method. The findings of this study will find direct applications in molecular physics.

A class of solvable multidimensional stopping problems in the presence of Knightian uncertainty

We investigate the impact of Knightian uncertainty on the optimal timing policy of an ambiguity-averse decision-maker in the case where the underlying factor dynamics follow a multidimensional Brownian motion and the exercise payoff depends on either a linear combination of the factors or the radial part of the driving factor dynamics. We present a general characterization of the value of the optimal timing policy and the worst-case measure in terms of a family of explicitly identified excessive functions generating an appropriate class of supermartingales. In line with previous findings based on linear diffusions, we find that ambiguity accelerates timing in comparison with the unambiguous setting. Somewhat surprisingly, we find that ambiguity may lead to stationarity in models which typically do not possess stationary behavior. In this way, our results indicate that ambiguity may act as a stabilizing mechanism.

Research of restrained bending of aircraft parts with curved sides

In the article the authors present a method of restrained elastomer bending of aircraft sheet parts with curved sides. Manufacturing of a part is carried out in two transitions; as a result of the first transition a part with thinning in the radial part is obtained, the second transition is carried out on the mold block of reduced height, as a result of which the resulting wave of excess material deforms along the radius of the bending mandrel. In the finished part, we can observe an increase in the thickness of the workpiece in the zone of the bend radius. Numerical studies of the process were conducted using the ANSYS/LS-DYNA software complex. As part of the study, the process flow model was worked out, the distribution of thickness of the material of the part over the entire surface under consideration was obtained, and graphs were plotted showing the elastomer pressure distributions and the deformation of the material of the part at characteristic points.

ANALYTICAL SOLUTION OF SCHRÖDINGER EQUATION IN BISPHERICAL COORDINATE FOR MOBIUS SQUARE PLUS MODIFIED YUKAWA POTENTIAL USING NIKIFOROV UVAROV FUNCTIONAL ANALYSIS (NUFA) METHOD WITH ITS THERMODYNAMICS PROPERTIES FOR DIATOMIC MOLECULES

Background: The analytical solution of the Schrödinger equation in bispherical coordinates has attracted a great deal of interest for theoretical physics researchers in the branch of quantum physics. The energy and wave function are solutions of the Schrödinger equation which are very important because it contains all necessary information regarding the behavior of quantum systems. Aim: This study aimed to obtain energy, radial wave functions and thermodynamic properties for diatomic molecules from the radial part of the Schrödinger equation in bispherical coordinates for the modified Mobius square plus Yukawa potential using the Nikiforov Uvarov Functional Analysis (NUFA) method. Methods: The variable separation method was applied to reduce the Schrodinger equation in bispherical coordinates to the radial part and angular part Schrodinger equation. The Schrodinger equation of the radial part in bispherical coordinates was solved using the Nikiforov Uvarov Functional Analysis (NUFA) method to obtain the energy equation and radial wave function. Furthermore, the vibrational partition function 𝑍 was obtained from the energy equation. The vibrational mean energy 𝑈, vibrational specific heat 𝐶, vibrational free energy 𝐹, and vibrational entropy 𝑆 were obtained from the vibrational partition function 𝑍. Results and Discussion: The results showed that the increase of parameters of 𝑛 and 𝛼 caused the decrease of energy, but the increase of parameters of 𝐿 and 𝑚0 caused the increase of energy. The radial quantum number 𝑛 and the potential range 𝛼 had the most effect to the wave functions. The parameters 𝑛𝑚𝑎𝑥, 𝑇, and 𝛼 had effect to the vibrational partition function 𝑍, vibrational mean energy 𝑈, vibrational specific heat 𝐶, vibrational free energy 𝐹, and vibrational entropy 𝑆. Conclusions: From the results of this study, it can be concluded that the energy, radial wave function, and thermodynamic properties for diatomic molecules have been obtained using the Nikiforov Uvarov Functional Analysis (NUFA) method.

$$\alpha $$-attractors from supersymmetry breaking

We construct new models of inflation and spontaneous supersymmetry breaking in de Sitter vacuum, with a single chiral superfield, where inflaton is the superpartner of the goldstino. Our approach is based on hyperbolic Kähler geometry, and a gauged (non-axionic) $$U(1)_R$$ U ( 1 ) R symmetry rotating the chiral scalar field by a phase. The $$U(1)_R$$ U ( 1 ) R gauge field combines with the angular component of the chiral scalar to form a massive vector, and single-field inflation is driven by the radial part of the scalar. We find that in a certain parameter range they can be approximated by simplest Starobinsky-like (E-model) $$\alpha $$ α -attractors, thus predicting $$n_s$$ n s and r within $$1\sigma $$ 1 σ CMB constraints. Supersymmetry (and R-symmetry) is broken at a high scale with the gravitino mass $$m_{3/2} > rsim 10^{14}$$ m 3 / 2 ≳ 10 14 GeV, and the fermionic sector also includes a heavy spin-1/2 field. In all the considered cases the inflaton is the lightest field of the model.

The application bispherical coordinate in Schrödinger equation for Mobius square plus modified Yukawa potential using Nikiforov Uvarov Functional Analysis (NUFA) method

<p class="Abstract">The application bispherical coordinates in Schrödinger equation for the Mobius square plus modified Yukawa potential have been obtained. The Schrödinger equation in bispherical coordinates for the separable Mobius square plus modified Yukawa potential consisting of the radial part and the angular part for the Mobius square plus modified Yukawa potential is solved using the variable separation method to reduce it to the radial part and angular part Schrödinger equation. The aim of this study was to solve the Schrödinger's equation of radial in bispherical coordinates for the Mobius square plus modified Yukawa potential using the Nikiforov Uvarov Functional Analysis (NUFA) method. Nikiforov Uvarov Functional Analysis (NUFA) method used to obtained energy spectrum equation and wave function for the Mobius square plus modified Yukawa potential. The result of energy spectrum equation for Mobius square plus modified Yukawa potential can be shown in Equation (50). The result of un-normalized wave function equation for Mobius square plus modified Yukawa potential can be shown in Table 1.</p>

Vibrational-rotational spectra of even–even nuclei with quadrupole and octupole deformations

Vibrational-rotation levels of the yrast and first nonyrast alternating-parity bands of the lanthanide [Formula: see text]Nd, [Formula: see text]Sm, [Formula: see text]Gd, [Formula: see text]Er and actinide [Formula: see text]Th, [Formula: see text]U, [Formula: see text]Pu nuclei are studied in the framework of a nonadiabatic collective model of even–even nuclei with quadrupole and octupole deformations. The theoretical spectra are obtained through the use of Gauss and harmonic-oscillator (HO) potentials in the radial part of the Schrödinger equation which is taken in polar coordinates. The change of the surface deformation of the nucleus with the collective excitation energy is taken into account. The [Formula: see text] staggering structure of the yrast alternating-parity bands is also considered. The theoretically obtained energy bands and staggering diagrams are in good agreement with the corresponding experimental data and point out the soft character of the collective quadrupole–octupole deformation mode manifesting in these nuclei.

Gender Difference Analysis of Chinese Han Youth Based on Fingerprint Ridge Density

Objective To discuss whether there are differences in fingerprint ridge density between the males and the females and what the specific differences are. Method A total of 120 males and 120 females (all were college students in Fujian) were selected, and the fingerprint ridge densities of these 240 Han youths were counted. According to Acree method, the radial upper part of the core region of the fingerprint center was selected for analysis, because the fingerprint pattern types in this region all presented similar ridges. This method was used to isolate the ridge in a certain area, so as to facilitate the counting. A 5mm×5mm grid was designated as a counting area on the middle radial part of the fingerprint for identification. Fingerprint ridges in the unit area were counted, then the average was calculated, and finally SPSS software was used to process and analyze all the data obtained. Result For the females, the average ten-fingerprint ridge density was basically above 14 ridges/ 25mm2; and for the males, it was basically below 14.5 ridges/25mm2. Conclusion There are some differences in the density of ten-fingerprints between men and the females, and the females’ is generally higher than that of the males.