scholarly journals Mass Spectrum of Mesons via the WKB Approximation Method

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Ekwevugbe Omugbe ◽  
Omosede E. Osafile ◽  
Michael C. Onyeaju
Keyword(s):  
Approximation Method ◽  
Mass Spectra ◽  
Turning Point ◽  
Approximation Scheme ◽  
Wkb Approximation ◽  
Quadratic Potential ◽  
Energy Eigenvalues ◽  
Type Approximation ◽  
Special Cases ◽  
Good Agreement

In this paper, we demonstrated that the multiple turning point problems within the framework of the Wentzel-Kramers-Brillouin (WKB) approximation method can be reduced to two turning point one for a nonsymmetric potential function by using an appropriate Pekeris-type approximation scheme. We solved the Schrödinger equation with the Killingbeck potential plus an inversely quadratic potential (KPIQP) function. The special cases of the modeled potential are discussed. We obtained the energy eigenvalues and the mass spectra of the heavy QQ¯ and heavy-light Qq¯ mesons systems. The results in this present work are in good agreement with the results obtained by other analytical methods and available experimental data in the literature.

scholarly journals Non-relativistic Energy Spectrum of the Deng-Fan Oscillator via the WKB Approximation Method

2020 ◽  
pp. 26-36 ◽  
Author(s):  
Ekwevugbe Omugbe
Keyword(s):  
Energy Spectrum ◽  
Approximation Method ◽  
Analytical Methods ◽  
Approximation Scheme ◽  
Wkb Approximation ◽  
Relativistic Energy ◽  
Implicit Equation ◽  
Energy Eigenvalues ◽  
Radial Schrödinger Equation ◽  
Interacting Systems

The energy spectrum of the radial Schrodinger equation with the molecular Deng Fan potential has been obtained through the WKB approximation scheme. The radial WKB solution yields a transcendental or an implicit equation. The energy eigenvalues for non-physical and real molecular interacting systems are presented. In comparison with the numerical eigenvalues obtained with MATHEMATICA 3.0 package, the WKB approximation method produces improved results over the results obtained with other analytical methods in the literature.

scholarly journals The Nonrelativistic Scattering States of the Deng-Fan Potential

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Bentol Hoda Yazarloo ◽  
Liangliang Lu ◽  
Guanghui Liu ◽  
Saber Zarrinkamar ◽  
Hassan Hassanabadi
Keyword(s):  
Approximation Scheme ◽  
Wave Functions ◽  
Energy Eigenvalues ◽  
Scattering States ◽  
Special Cases ◽  
Scattering State ◽  
Term Energy ◽  
Scattering Phase ◽  
Scattering Phase Shifts ◽  
Nonrelativistic Scattering

The approximately analytical scattering state solution of the Schrodinger equation is obtained for the Deng-Fan potential by using an approximation scheme to the centrifugal term. Energy eigenvalues, normalized wave functions, and scattering phase shifts are calculated. We consider and verify two special cases: thel=0and thes-wave Hulthén potential.

scholarly journals Spin Splitting Spectroscopy of Heavy Quark and Antiquarks Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Hesham Mansour ◽  
Ahmed Gamal ◽  
M. Abolmahassen
Keyword(s):  
Mass Spectra ◽  
Bound States ◽  
Good Accuracy ◽  
Theoretical Calculations ◽  
Spin Splitting ◽  
Energy Eigenvalues ◽  
Central Case ◽  
Nu Method ◽  
Better Than ◽  
Good Agreement

Phenomenological potentials describe the quarkonium systems like c c ¯ , b b , ¯   and   b ¯ c where they give a good accuracy for the mass spectra. In the present work, we extend one of our previous works in the central case by adding spin-dependent terms to allow for relativistic corrections. By using such terms, we get better accuracy than previous theoretical calculations. In the present work, the mass spectra of the bound states of heavy quarks   c c ¯ , b b ¯ , and 𝐵𝑐 mesons are studied within the framework of the nonrelativistic Schrödinger equation. First, we solve Schrödinger’s equation by Nikiforov-Uvarov (NU) method. The energy eigenvalues are presented using our new potential. The results obtained are in good agreement with the experimental data and are better than the previous theoretical estimates.

scholarly journals APPROXIMATE ℓ-STATE SOLUTION OF TIME INDEPENDENT SCHRÖDINGER WAVE EQUATION WITH MODIFIED MÖBIUS SQUARED POTENTIAL PLUS HULTHÉN POTENTIAL

2020 ◽  
Vol 4 (2) ◽  
pp. 425-435
Author(s):  
Dlama Yabwa ◽  
Eyube E.S ◽  
Yusuf Ibrahim
Keyword(s):  
State Energy ◽  
Approximation Scheme ◽  
Bound State ◽  
Wave Functions ◽  
Bound State Energy ◽  
Hulthén Potential ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Type Approximation ◽  
Hulthen Potential

In this work we have applied ansatz method to solve for the approximate ℓ-state solution of time independent Schrödinger wave equation with modified Möbius squared potential plus Hulthén potential to obtain closed form expressions for the energy eigenvalues and normalized radial wave-functions. In dealing with the spin-orbit coupling potential of the effective potential energy function, we have employed the Pekeris type approximation scheme, using our expressions for the bound state energy eigenvalues, we have deduced closed form expressions for the bound states energy eigenvalues and normalized radial wave-functions for Hulthén potential, modified Möbius square potential and Deng-Fan potential. Using the value 0.976865485225 for the parameter ω, we have computed bound state energy eigenvalues for various quantum states (in atomic units). We have also computed bound state energy eigenvalues for six diatomic molecules: HCl, LiH, TiH, NiC, TiC and ScF. The results we obtained are in near perfect agreement with numerical results in the literature and a clear demonstration of the superiority of the Pekeris-type approximation scheme over the Greene and Aldrich approximation scheme for the modified Möbius squares potential plus Hulthén potential.

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 A SEMIRELATIVISTIC TREATMENT OF SPINLESS PARTICLES SUBJECT TO THE YUKAWA POTENTIAL WITH ARBITRARY ANGULAR MOMENTA

2012 ◽  
Vol 21 (02) ◽  
pp. 1250016 ◽  
Author(s):  
MAJID HAMZAVI ◽  
SAMEER M. IKHDAIR ◽  
M. SOLAIMANI
Keyword(s):  
State Energy ◽  
Approximation Scheme ◽  
Yukawa Potential ◽  
Bound State ◽  
Nonrelativistic Limit ◽  
Centrifugal Term ◽  
Angular Momenta ◽  
Special Cases ◽  
Analytical Expressions ◽  
Good Agreement

We obtain analytical solutions of the two-body spinless Salpeter (SS) equation with the Yukawa potential within the conventional approximation scheme to the centrifugal term for any l-state. The semirelativistic bound-state energy spectra and the corresponding normalized wave functions are calculated by means of the Nikiforov–Uvarov (NU) method. We also obtain the numerical energy spectrum of the SS equation without any approximation to centrifugal term for the same potential and compare them with the approximated numerical ones obtained from the analytical expressions. It is found that the exact numerical results are in good agreement with the approximated ones for the lower energy states. Special cases are treated like the nonrelativistic limit and the solution for the Coulomb problem.

scholarly journals Study on the Applicability of Varshni Potential to Predict the Mass Spectra of the Quark-Antiquark Systems in a Non-relativistic Framework

2021 ◽  
Vol 14 (4) ◽  
pp. 339-347
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Mass Spectra ◽  
Laguerre Polynomials ◽  
Heavy Meson ◽  
Energy Eigenvalues ◽  
Relativistic Regime ◽  
Uvarov Method ◽  
Relativistic Framework ◽  
Good Agreement

Abstract: In this work, we obtain the Schrödinger equation solutions for the Varshni potential using the Nikiforov-Uvarov method. The energy eigenvalues are obtained in non-relativistic regime. The corresponding eigenfunction is obtained in terms of Laguerre polynomials. We applied the present results to calculate heavy-meson masses of charmonium cc ¯ and bottomonium bb ¯. The mass spectra for charmonium and bottomonium multiplets have been predicted numerically. The results are in good agreement with experimental data and the works of other researchers. Keywords: Schrödinger equation, Varshni potential, Nikiforov-Uvarov method, Heavy meson. PACs: 14.20.Lq; 03.65.-w; 14.40.Pq; 11.80.Fv.

scholarly journals Eigensolutions of the N-dimensional Schrödinger equation interacting with Varshni-Hulthén potential model

2021 ◽  
Vol 67 (2 Mar-Apr) ◽  
pp. 193
Author(s):  
E. P. Inyang ◽  
E. S. William ◽  
J. A. Obu
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Approximation Scheme ◽  
Jacobi Polynomials ◽  
Hulthén Potential ◽  
Centrifugal Barrier ◽  
Energy Eigenvalues ◽  
Hulthen Potential ◽  
Special Cases ◽  
Uvarov Method

Analytical solutions of the N-dimensional Schrödinger equation for the newly proposed Varshni-Hulthén potential are obtained within the framework of Nikiforov-Uvarov method by using Greene-Aldrich approximation scheme to the centrifugal barrier. The numerical energy eigenvalues and the corresponding normalized eigenfunctions are obtained in terms of Jacobi polynomials. Special cases of the potential are equally studied and their numerical energy eigenvalues are in agreement with those obtained previously with other methods. However, the behavior of the energy for the ground state and several excited states is illustrated graphically.

scholarly journals Arbitrary l-solutions of the Schrödinger equation interacting with Hulthén – Hellmann potential model

2020 ◽  
Vol 66 (6 Nov-Dec) ◽  
pp. 730 ◽  
Author(s):  
E. S. William ◽  
E. P. Inyang ◽  
E. A. Thompson
Keyword(s):  
Schrödinger Equation ◽  
Quantum State ◽  
Schrodinger Equation ◽  
Potential Model ◽  
Bound State ◽  
Energy Eigenvalues ◽  
Special Cases ◽  
Radial Schrödinger Equation ◽  
Hellmann Potential ◽  
Good Agreement

In this study, we obtained bound state solutions of the radial Schrödinger equation by the superposition of Hulthén plus Hellmann potential within the framework of Nikiforov-Uvarov (NU) method for an arbitrary  - states. The corresponding normalized wave functions expressed in terms of Jacobi polynomial for a particle exposed to this potential field was also obtained. The numerical energy eigenvalues for different quantum state have been computed. Six special cases are also considered and their energy eigenvalues are obtained. Our results are found to be in good agreement with the results in literature. The behavior of energy in the ground and excited state for different quantum state are studied graphically.

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