Calculation of the energy eigenvalues of the Yukawa potential via variation principle

2020 ◽  
Vol 29 (09) ◽  
pp. 2050067
Author(s):  
E. Yazdankish
Keyword(s):  
Solid State ◽  
Analytical Solution ◽  
Yukawa Potential ◽  
Wave Functions ◽  
Variation Principle ◽  
Centrifugal Term ◽  
Energy Eigenvalues ◽  
Numerical Result ◽  
Yukawa Potentials ◽  
Uvarov Method

The Yukawa potential has an important and significant rule in some branches of physics such as nuclear, plasma and solid state. However, there is no analytical solution for Schrödinger equation with this potential without approximation, therefore, other ways, such as numerical, perturbation, variation and so on, are taken to deal with this potential. In this work, the variation principle is taken to obtain some of its energy eigenvalues. In the arbitrary [Formula: see text]-state, the Yukawa potentials with centrifugal term are taken together as effective potential and then by choosing the wave functions of the Hulthen potential as trial function which are obtained in this work from the Nikiforov–Uvarov method, and then by applying the variation principle, the energy eigenvalues are obtained. After that, the result is compared with the former numerical result. The comparison shows excellent agreement between our result and the former numerical ones.

Relativistic symmetries of fermions in the background of the inversely quadratic Yukawa potential with Yukawa potential as a tensor

2014 ◽  
Vol 92 (1) ◽  
pp. 51-58
Author(s):  
Majid Hamzavi ◽  
Sameer M. Ikhdair
Keyword(s):  
Yukawa Potential ◽  
Bound State ◽  
Arbitrary Spin ◽  
Tensor Interaction ◽  
Wave Functions ◽  
Energy Eigenvalues ◽  
Yukawa Tensor Interaction ◽  
Uvarov Method ◽  
Spinor Wave ◽  
Component Spinor

In the presence of spin and pseudo-spin symmetries, we obtain approximate analytical bound state solutions to the Dirac equation with scalar–vector inverse quadratic Yukawa potential including a Yukawa tensor interaction for any arbitrary spin–orbit quantum number, κ. The energy eigenvalues and their corresponding two-component spinor wave functions are obtained in closed form using the parametric Nikiforov–Uvarov method. It is noticed that the tensor interaction removes the degeneracy in the spin and p-spin doublets. Some numerical results are obtained for the lowest energy states within spin and pseudo-spin symmetries.

Duffin–Kemmer–Petiau oscillator in the presence of a cosmic screw dislocation

2020 ◽  
Vol 35 (30) ◽  
pp. 2050195
Author(s):  
Soroush Zare ◽  
Hassan Hassanabadi ◽  
Marc de Montigny
Keyword(s):  
Elastic Medium ◽  
Screw Dislocation ◽  
Topological Defect ◽  
Potential Functions ◽  
Wave Functions ◽  
Screw Dislocations ◽  
Energy Eigenvalues ◽  
Heun Function ◽  
Uvarov Method ◽  
The Impact

We examine the behavior of spin-zero bosons in an elastic medium which possesses a screw dislocation, which is a type of topological defect. Therefore, we solve analytically the Duffin–Kemmer–Petiau (DKP) oscillator for bosons in the presence of a screw dislocation with two types of potential functions: Cornell and linear-plus-cubic potential functions. For each of these functions, we analyze the impact of screw dislocations by determining the wave functions and the energy eigenvalues with the help of the Nikiforov–Uvarov method and Heun function.

scholarly journals Pseudospin and Spin Symmetric Solutions of the Dirac Equation: Hellmann Potential,Wei–Hua Potential, Varshni Potential

2014 ◽  
Vol 69 (3-4) ◽  
pp. 163-172 ◽  
Author(s):  
Altuğ Arda ◽  
Ramazan Sever
Keyword(s):  
Dirac Equation ◽  
Analytical Solutions ◽  
Energy Eigenvalue ◽  
Wave Functions ◽  
K Value ◽  
Energy Eigenvalues ◽  
Approximate Analytical Solutions ◽  
Hellmann Potential ◽  
Uvarov Method ◽  
Spinor Wave

Approximate analytical solutions of the Dirac equation are obtained for the Hellmann potential, the Wei-Hua potential, and the Varshni potential with any k-value for the cases having the Dirac equation pseudospin and spin symmetries. Closed forms of the energy eigenvalue equations and the spinor wave functions are obtained by using the Nikiforov-Uvarov method and some tables are given to see the dependence of the energy eigenvalues on different quantum number pairs (n;κ).

scholarly journals Некоммутативная задача Ландау о фазовом пространстве при наличии минимальной длины

2020 ◽  
pp. 188-198
Author(s):  
F.A. Dossa ◽  
J.T. Koumagnon ◽  
J.V. Hounguevou ◽  
G.Y.H. Avossevou
Keyword(s):  
Electromagnetic Field ◽  
Phase Space ◽  
Momentum Space ◽  
Hypergeometric Functions ◽  
Heisenberg Algebra ◽  
Minimal Length ◽  
Wave Functions ◽  
Energy Eigenvalues ◽  
Uvarov Method

The deformed Landau problem under a electromagnetic field is studied, where the Heisenberg algebra is constructed in detail in non-commutative phase space in the presence of a minimal length. We show that, in the presence of a minimal length, the momentum space is more practical to solve any problem of eigenvalues. From the Nikiforov-Uvarov method, the energy eigenvalues are obtained and the corresponding wave functions are expressed in terms of hypergeometric functions. The fortuitous degeneration observed in the spectrum shows that the formulation of the minimal length complements that of the non-commutative phase space. Изучается деформированная задача Ландау в электромагнитном поле, в которой алгебра Гейзенберга подробно строится в некоммутативном фазовом пространстве при наличии минимальной длины. Мы показываем, что при наличии минимальной длины импульсное пространство более практично для решения любой проблемы собственных значений. С помощью метода Никифорова-Уварова получаются собственные значения энергии, а соответствующие волновые функции выражаются через гипергеометрические функции. Случайное вырождение, наблюдаемое в спектре, показывает, что формулировка минимальной длины дополняет формулировку некоммутативного фазового пространства.

scholarly journals Pseudo-spin Symmetry for Relativistic-Hyperbolic Problem and Tensor Potential

2011 ◽  
Vol 3 (3) ◽  
pp. 493-500 ◽  
Author(s):  
M. Eshghi
Keyword(s):  
Dirac Equation ◽  
Relativistic Equation ◽  
Spin Symmetry ◽  
Numerical Results ◽  
Wave Functions ◽  
Hyperbolic Problem ◽  
Energy Eigenvalues ◽  
Tensor Potential ◽  
Hyperbolic Potential ◽  
Uvarov Method

We study the relativistic equation of spin-1/2 particles under the hyperbolic potential and a Coulomb-like tensor potential. By using the generalized parametric of the Nikiforov-Uvarov method and the pseudo-spin symmetry, we obtain the energy eigenvalues equation and the corresponding unnormalized wave functions. Some numerical results are given, too.Keywords: Dirac equation; Tensor potential; Pseudo-spin symmetry; Nikiforov-Uvarov.© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserveddoi:10.3329/jsr.v3i3.8071               J. Sci. Res. 3 (3), 503-510 (2011

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.

Makarov potential in relativistic equation via Laplace transformation approach

2013 ◽  
Vol 91 (1) ◽  
pp. 71-74 ◽  
Author(s):  
Mahdi Eshghi
Keyword(s):  
Laplace Transformation ◽  
Pseudospin Symmetry ◽  
Relativistic Equation ◽  
Wave Functions ◽  
Hole State ◽  
Shape Invariance ◽  
Energy Eigenvalues ◽  
Special Cases ◽  
The Laplace Transform ◽  
Uvarov Method

Exact solutions and corresponding normalized eigenfunctions of the Dirac equation are studied for the Makarov potential by using the Laplace transform approach under the pseudospin symmetry. By using the ideas of SUSY and shape invariance, we obtain the energy eigenvalues equation. The wave functions of the angle part are obtained by using the Nikiforov–Uvarov method, too. Finally, we also discuss the special cases of this potential and the valence energy states can be produced from our solution for the hole state by taking appropriate transformation of parameters.

scholarly journals Aspect Ratio Effect of Vertical Lid Driven Chamber Having a Centered Conducting Solid on Mixed Magnetoconvection

2011 ◽  
Vol 3 (3) ◽  
pp. 501-513 ◽  
Author(s):  
R. Nasrin
Keyword(s):  
Dirac Equation ◽  
Aspect Ratio ◽  
Relativistic Equation ◽  
Spin Symmetry ◽  
Wave Functions ◽  
Ratio Effect ◽  
Energy Eigenvalues ◽  
Tensor Potential ◽  
Hyperbolic Potential ◽  
Uvarov Method

We study the relativistic equation of spin-1/2 particles under the hyperbolic potential and a Coulomb-like tensor potential. By using the generalized parametric of the Nikiforov-Uvarov method and the pseudo-spin symmetry, we obtain the energy eigenvalues equation and the corresponding unnormalized wave functions. Some numerical results are given, too.Keywords: Dirac equation; Tensor potential; Pseudo-spin symmetry; Nikiforov-Uvarov.© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserveddoi:10.3329/jsr.v3i3.8071               J. Sci. Res. 3 (3), 503-510 (2011)

scholarly journals Solution of the Schrödinger equation with inversely quadratic Yukawa potential (IQYP) plus Kratzer-Fues (KFP) potential using the WKB quantum mechanical formalism

2019 ◽  
Vol 44 (3) ◽  
pp. 50-55 ◽  
Author(s):  
Benedict Iserom Ita ◽  
Hitler Louis ◽  
Nelson Nzeata-Ibe
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Yukawa Potential ◽  
Research Work ◽  
Bound State ◽  
Wave Functions ◽  
Energy Eigenvalues ◽  
Mechanical Formalism ◽  
Modified Kratzer Potential ◽  
Quantum Mechanical Formalism

The main objective of this research work is theoretical investigate the bound state solutions of the non-relativistic Schrödinger equation with a mixed potential composed of the Inversely Quadratic Yukawa/Attractive Coulomb potential plus a Modified Kratzer potential (IQYCKFP) by utilizing the Wentzel-Kramers-Brillouin (WKB) quantum theoretical formalism. The energy eigenvalues and its associated wave functions have successfully been obtained sequel to certain diatomic molecules includes; HCL, HBr, LiH.

scholarly journals Approximate κ-state solutions to the Dirac Mobius square – Yukawa and Mobius square – quasi Yukawa problems under pseudospin and spin symmetry limits with Coulomb-like tensor interaction

2013 ◽  
Vol 91 (7) ◽  
pp. 560-575 ◽  
Author(s):  
Akpan N. Ikot ◽  
E. Maghsoodi ◽  
Akaninyene D. Antia ◽  
S. Zarrinkamar ◽  
H. Hassanabadi
Keyword(s):  
Spin Symmetry ◽  
Arbitrary Spin ◽  
Tensor Interaction ◽  
Wave Functions ◽  
Symmetry Limit ◽  
Energy Eigenvalues ◽  
Interaction Term ◽  
Yukawa Potentials ◽  
Spin Symmetry Limit ◽  
Coulomb Potentials

In this paper, we present the Dirac equation for the Mobius square – Yukawa potentials including the tensor interaction term within the framework of pseudospin and spin symmetry limit with arbitrary spin–orbit quantum number, κ. We obtain the energy eigenvalues and the corresponding wave functions using the supersymmetry method. The limiting cases of the problem, which reduce to the Deng-Fan, Yukawa, and Coulomb potentials, are discussed.

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