scholarly journals Quarkonium masses in a hot QCD medium using conformable fractional of the Nikiforov–Uvarov method

2019 ◽  
Vol 34 (31) ◽  
pp. 1950201
Author(s):  
M. Abu-Shady
Keyword(s):  
Order Parameter ◽  
Dimensional Space ◽  
Binding Energies ◽  
Heavy Quarkonium ◽  
Energy Eigenvalues ◽  
Debye Mass ◽  
Higher Dimensional ◽  
Radial Schrödinger Equation ◽  
Uvarov Method ◽  
Nu Method

By using the conformable fractional of the Nikiforov–Uvarov (CF–NU) method, the radial Schrödinger equation is analytically solved. The energy eigenvalues and corresponding functions are obtained, in which the dependent temperature potential is employed. The effect of fraction-order parameter is studied on the heavy-quarkonium masses such as charmonium and bottomonium in a hot QCD medium in the 3D and the higher-dimensional space. This paper discusses the flavor dependence of their binding energies and explores the nature of dissociation by employing the perturbative, nonperturbative, and the lattice-parametrized form of the Debye masses in the medium-modified potential. A comparison is studied with recent works. We conclude that the fractional-order plays an important role in a hot QCD medium in the 3D with consideration of a form of the Debye mass.

Approximate Ro-Vibrational Spectrum of the Modified Rosen–Morse Molecular Potential Using the Nikiforov–Uvarov Method

2013 ◽  
Vol 68 (6-7) ◽  
pp. 427-432 ◽  
Author(s):  
Ali Akbar Rajabi ◽  
Majid Hamzavi
Keyword(s):  
Vibrational Spectrum ◽  
Schrodinger Equation ◽  
Approximation Scheme ◽  
Centrifugal Term ◽  
Energy Eigenvalues ◽  
Molecular Potential ◽  
Radial Schrödinger Equation ◽  
Uvarov Method ◽  
Nu Method ◽  
Good Agreement

By using the Nikiforov-Uvarov (NU) method and a new approximation scheme to the centrifugal term, we obtained the solutions of the radial Schrödinger equation (SE) for the modified Rosen- Morse (mRM) potential. In this paper, we get the approximate energy eigenvalues and show that the results are in good agreement with those obtained before. Eigenfunctions are also presented for completeness.

scholarly journals Binding Energies and Dissociation Temperatures of Heavy Quarkonia at Finite Temperature and Chemical Potential in the N-Dimensional Space

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
M. Abu-Shady ◽  
T. A. Abdel-Karim ◽  
E. M. Khokha
Keyword(s):  
Finite Temperature ◽  
Chemical Potential ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Binding Energies ◽  
Heavy Quarkonia ◽  
Energy Eigenvalues ◽  
Cornell Potential ◽  
Radial Schrödinger Equation ◽  
Three Dimensional Space

The N-dimensional radial Schrödinger equation has been solved using the analytical exact iteration method (AEIM), in which the Cornell potential is generalized to finite temperature and chemical potential. The energy eigenvalues have been calculated in the N-dimensional space for any state. The present results have been applied for studying quarkonium properties such as charmonium and bottomonium masses at finite temperature and quark chemical potential. The binding energies and the mass spectra of heavy quarkonia are studied in the N-dimensional space. The dissociation temperatures for different states of heavy quarkonia are calculated in the three-dimensional space. The influence of dimensionality number (N) has been discussed on the dissociation temperatures. In addition, the energy eigenvalues are only valid for nonzero temperature at any value of quark chemical potential. A comparison is studied with other recent works. We conclude that the AEIM succeeds in predicting the heavy quarkonium at finite temperature and quark chemical potential in comparison with recent works.

SOLUTIONS OF THE SCHRODINGER EQUATION WITH INVERSELY QUADRATIC YUKAWA PLUS WOODS-SAXON POTENTIAL USING NIKIFOROV-UVAROV METHOD

2015 ◽  
Vol 8 (2) ◽  
pp. 2094-2098
Author(s):  
Benedict Ita ◽  
A. I. Ikeuba ◽  
O. Obinna
Keyword(s):  
State Energy ◽  
Jacobi Polynomials ◽  
Bound State ◽  
Negative Energy ◽  
Saxon Potential ◽  
Energy Eigenvalues ◽  
Eigen Values ◽  
Uvarov Method ◽  
Special Case ◽  
Nu Method

The solutions of the SchrÓ§dinger equation with inversely quadratic Yukawa plus Woods-Saxon potential (IQYWSP) have been presented using the parametric Nikiforov-Uvarov (NU) method. The bound state energy eigenvalues and the corresponding un-normalized eigen functions are obtained in terms of Jacobi polynomials. Also, a special case of the potential has been considered and its energy eigen values obtained. The result of the work could be applied to molecules moving under the influence of IQYWSP potential as negative energy eigenvalues obtained indicate a bound state system.

scholarly journals Multidimensional Schrödinger Equation and Spectral Properties of Heavy-Quarkonium Mesons at Finite Temperature

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
M. Abu-Shady
Keyword(s):  
Schrödinger Equation ◽  
Quark Gluon Plasma ◽  
Plasma Diagnostics ◽  
Finite Temperature ◽  
Schrodinger Equation ◽  
Gluon Plasma ◽  
Wave Functions ◽  
Heavy Quarkonium ◽  
Energy Eigenvalues ◽  
Radial Schrödinger Equation

TheN-radial Schrödinger equation is analytically solved at finite temperature. The analytic exact iteration method (AEIM) is employed to obtain the energy eigenvalues and wave functions for all statesnandl. The application of present results to the calculation of charmonium and bottomonium masses at finite temperature is also presented. The behavior of the charmonium and bottomonium masses is in qualitative agreement with other theoretical methods. We conclude that the solution of the Schrödinger equation plays an important role at finite temperature that the analysis of the quarkonium states gives a key input to quark-gluon plasma diagnostics.

scholarly journals ANALYTICAL SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH THE WOODS–SAXON POTENTIAL FOR ARBITRARY l STATE

2009 ◽  
Vol 18 (03) ◽  
pp. 631-641 ◽  
Author(s):  
V. H. BADALOV ◽  
H. I. AHMADOV ◽  
A. I. AHMADOV
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
State Energy ◽  
Bound State ◽  
Saxon Potential ◽  
Energy Eigenvalues ◽  
Quantum Numbers ◽  
Radial Schrödinger Equation ◽  
Uvarov Method ◽  
Pekeris Approximation

In this work, the analytical solution of the radial Schrödinger equation for the Woods–Saxon potential is presented. In our calculations, we have applied the Nikiforov–Uvarov method by using the Pekeris approximation to the centrifugal potential for arbitrary l states. The bound state energy eigenvalues and corresponding eigenfunctions are obtained for various values of n and l quantum numbers.

Eigensolutions and theoretic quantities under the nonrelativistic wave equation

2020 ◽  
Vol 19 (02) ◽  
pp. 2050007
Author(s):  
C. A. Onate ◽  
L. S. Adebiyi ◽  
D. T. Bankole
Keyword(s):  
Wave Function ◽  
Energy Equation ◽  
Radial Wave Function ◽  
Tsallis Entropy ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Screening Parameter ◽  
Radial Schrödinger Equation ◽  
Information Energy ◽  
Uvarov Method

The radial Schrödinger equation was solved with the combination of three important potentials with [Formula: see text] as deformed parameter via the parametric Nikiforov–Uvarov method and the energy equation as well as the corresponding normalized radial wave function were obtained in close and compact form. The energy equation obtained was used to study eight molecules. The effect of the deformed parameter on energy eigenvalues was also studied numerically. The subset of the combined potential was also studied numerically and the results were found to be in agreement with the previous results. To extend the application of our work, the wave function obtained was used to calculate some theoretic quantities such as the Tsallis entropy, Rényi entropy and information energy. By putting the Tsallis index to 2, we deduced the information energy from Tsallis entropy. Finally, the effect of the deformed parameter and screening parameter, respectively, on the theoretic quantities were also studied.

Melting of quarkonium in an anisotropic hot QCD medium in the presence of a generalized Debye screening mass and Nikiforov–Uvarov’s method

2020 ◽  
Vol 35 (21) ◽  
pp. 2050110
Author(s):  
M. Abu-shady ◽  
H. M. Fath-Allah
Keyword(s):  
Power Series ◽  
Anisotropic Medium ◽  
Isotropic Medium ◽  
Binding Energies ◽  
Anisotropic Plasma ◽  
Debye Screening ◽  
The Real ◽  
Radial Schrödinger Equation ◽  
Dissociation Temperature ◽  
Nu Method

Generalized temperature and anisotropy dependent Debye screening mass is introduced into the real part of a potential in an anisotropic plasma. The N-radial Schrödinger equation (SE) is approximately solved by using the Nikiforov–Uvarov (NU) method which based on the expansion of power series. Binding energies and dissociation temperatures of charmonium and bottomonium are calculated. In addition, we have calculated the screening mass values for different parameters. Comparing to their values in an isotropic medium, the charmonium and bottomonium binding energies within an anisotropic medium are found to be increased. Also, the dissociation temperatures of both the charmonium and the bottomonium within anisotropic environments appear larger relative to those found within an isotropic medium. Finally, one observes that in any medium the bottomonium dissociation temperature is higher than the charmonium one.

The search for fractional order in heavy quarkonia spectra

2019 ◽  
Vol 34 (10) ◽  
pp. 1950054 ◽  
Author(s):  
Ahmed Al-Jamel
Keyword(s):  
Fractional Order ◽  
Mass Spectra ◽  
Dimensional Space ◽  
Heavy Quarkonia ◽  
Eigenvalues And Eigenfunctions ◽  
Energy Eigenvalues ◽  
Dimension Formula ◽  
Fractional Models ◽  
Uvarov Method ◽  
Exact Energy

Using the concept of conformable fractional derivative, we study the properties of fractional [Formula: see text]-dimensional Schrödinger equation for the potential [Formula: see text]. The extended Nikiforov–Uvarov method is generalized to the fractional domain and then employed to obtain the analytic exact energy eigenvalues and eigenfunctions and their dependence on the fractional order [Formula: see text] and the dimension [Formula: see text]. To test its applicability, we apply the method on heavy quarkonia systems, and reproduce their mass spectra and fractional radial probabilities at different values of [Formula: see text] and [Formula: see text]. Comparing the mass spectra with the experimental data, we discuss to what extent fractional models can account for some features in the description of heavy quarkonia at certain dimensional space.

Celestial Tapestry

2020 ◽  
Author(s):  
Nicholas Mee
Keyword(s):  
Mathematics Curriculum ◽  
Dimensional Space ◽  
Golden Section ◽  
Single Point ◽  
Historical Context ◽  
Computer Art ◽  
Lightning Strike ◽  
Secret Message ◽  
Axiomatic Method ◽  
Higher Dimensional

Celestial Tapestry places mathematics within a vibrant cultural and historical context, highlighting links to the visual arts and design, and broader areas of artistic creativity. Threads are woven together telling of surprising influences that have passed between the arts and mathematics. The story involves many intriguing characters: Gaston Julia, who laid the foundations for fractals and computer art while recovering in hospital after suffering serious injury in the First World War; Charles Howard, Hinton who was imprisoned for bigamy but whose books had a huge influence on twentieth-century art; Michael Scott, the Scottish necromancer who was the dedicatee of Fibonacci’s Book of Calculation, the most important medieval book of mathematics; Richard of Wallingford, the pioneer clockmaker who suffered from leprosy and who never recovered from a lightning strike on his bedchamber; Alicia Stott Boole, the Victorian housewife who amazed mathematicians with her intuition for higher-dimensional space. The book includes more than 200 colour illustrations, puzzles to engage the reader, and many remarkable tales: the secret message in Hans Holbein’s The Ambassadors; the link between Viking runes, a Milanese banking dynasty, and modern sculpture; the connection between astrology, religion, and the Apocalypse; binary numbers and the I Ching. It also explains topics on the school mathematics curriculum: algorithms; arithmetic progressions; combinations and permutations; number sequences; the axiomatic method; geometrical proof; tessellations and polyhedra, as well as many essential topics for arts and humanities students: single-point perspective; fractals; computer art; the golden section; the higher-dimensional inspiration behind modern art.

scholarly journals Aperiodic Crystals

2014 ◽  
Vol 70 (a1) ◽  
pp. C1-C1 ◽  
Author(s):  
Ted Janssen ◽  
Aloysio Janner
Keyword(s):  
Physical Properties ◽  
Dimensional Space ◽  
X Rays ◽  
New Techniques ◽  
New Family ◽  
Modulated Phases ◽  
Open Questions ◽  
Higher Dimensional ◽  
Lattice Periodicity ◽  
Aperiodic Crystals

2014 is the International Year of Crystallography. During at least fifty years after the discovery of diffraction of X-rays by crystals, it was believed that crystals have lattice periodicity, and crystals were defined by this property. Now it has become clear that there is a large class of compounds with interesting properties that should be called crystals as well, but are not lattice periodic. A method has been developed to describe and analyze these aperiodic crystals, using a higher-dimensional space. In this lecture the discovery of aperiodic crystals and the development of the formalism of the so-called superspace will be described. There are several classes of such materials. After the incommensurate modulated phases, incommensurate magnetic crystals, incommensurate composites and quasicrystals were discovered. They could all be studied using the same technique. Their main properties of these classes and the ways to characterize them will be discussed. The new family of aperiodic crystals has led also to new physical properties, to new techniques in crystallography and to interesting mathematical questions. Much has been done in the last fifty years by hundreds of crystallographers, crystal growers, physicists, chemists, mineralogists and mathematicians. Many new insights have been obtained. But there are still many questions, also of fundamental nature, to be answered. We end with a discussion of these open questions.

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